I do not agree. I am an A class player. I got there by studying lots of tactics, but also by studying positional concepts at least as much. I've beaten other A class players by depriving the game of tactical complications. See http://chessskill.blogspot.com/2011/10/excelling-at-technical-chess.html for annotations to a game where I humbled a tactical monster with a simple queenside pawn majority.
Can you really become a class A player by studying tactics?

1800-2000 is Class A.
And no, it's just about impossible to make +1800 just on tactics alone. You have to learn how to set up the positions that lead to the winning tactics.

What is a Class A player, an American grade? And what are we talking about in terms of FIDE Elo?
Category 1 is equivalent (assuming FIDE ratings and USCF are comparable--it is well-known that at the highest levels, USCF run 50-100 above FIDE, but data on those below 2000 did not exist when these guidelines became commonplace).
"There are other parts of the game that players need to study, but for almost everybody below 1800, tactics is their biggest weakness and the easiest thing to improve!"
This is not a quote that says "Studying pure tactics will get you to 1800." It says "Until 1800, tactics is what you should be spending most of your time on." That's a very different claim.

Ziryab said, "Category 1 is equivalent (assuming FIDE ratings and USCF are comparable--it is well-known that at the highest levels, USCF run 50-100 above FIDE, but data on those below 2000 did not exist when these guidelines became commonplace). "
Ziryab, a First Category player used to be just below master strength. First Category was equivalent to expert in the US. Now, with the proliferation of "candidate master" titles in various national chess federations, it depends on the chess federation.

I think statements like these are fairly insidious. A 1300 may lose to a tactic... but he may have also gotten a permanently worse position 20 moves earlier and the tactic had been more or less inevitable since then. (Or even better, in another game with a bit of strategic knowledge he may have been able to convert the win / hold a draw without any effort). There are many factors that go into chess improvement and I think uhoh's comparison is a good one. Improving players may study lots of tactics, but they're also picking up other ideas along the way.
IMO if you aren't losing to tactics against your peers then you probably should study something else. Why? Other than diminishing returns for focusing on your strengths, players under 1800 are deficient in literally every aspect of the game... i.e. there's no type of study that won't help. A friend of mine would say about studying good books "it's worth at least 100 rating points [for class players]" no matter the subject. Vukovic's Art of Attack? 100 points, My System? 100 points. Silman's endgame book? 100 points.
I'm an expert player, and I got there by tactics, around 80% of my preparation, and a good 20% on others. I have never read any chess book or opening book.

I'm an expert player...
The USCF disagrees with you (1998), and you posted a tournament from three weeks ago where you lost rating points (1992).

Ziryab said, "Category 1 is equivalent (assuming FIDE ratings and USCF are comparable--it is well-known that at the highest levels, USCF run 50-100 above FIDE, but data on those below 2000 did not exist when these guidelines became commonplace). "
Ziryab, a First Category player is just below master strength. First Category is equivalent to expert in the US.
In the original Elo system, and in the Soviet system that set the standard for all of my early life, category 1 was below Candidate Master, and equivalent to A Class (minus the alleged rating inflation in the USA).
When Kasparov talks about becoming a category 1 player (age 8 or 9 as I recall) he is referring to a rating 1800-1999. In those days, one could not have a FIDE rating until over 2000.

Ok. When I spoke with Russians in the 1980s and 1990s, they considered 2000-2200 USCF to be First Category.
Perhaps that was a reflection of the fact that it was harder to become a Master in Russia than in FIDE.

They are factoring in the alleged inflation of USCF ratings. 2000-2200 USCF was considered 1900-2100 FIDE, officially, and most Russians would have considered the official estimates generous.
In other words, USCF experts were equal to Russian category 1, just as USCF masters would have been candidate masters in Russia.
No American, other than Fischer, could play 40 good moves with Vasily Smyslov and get that promised draw.

IMHO it's easily possible to make Class-A (USCF) and higher by concentrating on tactics. Again, IMHO I think that at least some if not most players with strong tactical ability will pick up some positional knowledge along the way even if most of it is picked up unintentionally. For instance, I think that strong tacticians will eventually become aware of some positional considerations such as weak pawns, open files, backrank weaknesses, etc. AND a lot of this boils down to semantics - again IMHO - for instance is being ahead or behind in development strictly a tactical consideration? What about proper piece placement and the pros and cons of offering or defending gambits? I'm not so sure there isn't a large gray area instead of an exact boundary where tactics end and positional chess begins.
On the other hand I'm sure it's better to study positional factors in addition to tactics, although I'm not sure if concentrating mostly (not exclusively) on tactics would be a gross blunder for Class-B and lower players as a means of improvement.
This is one topic in which people who are knowledgable about how students in general (and not just chessplayers) learn things and what study methods are most/least effective might have a lot to add - even if they don't play chess at all although that would certainly help to make their input more valuable if they did. For instance, the 2 co-authors of "Bobby Fischer Teaches Chess" were experts in programmed instruction, although one was also a chess master but the other co-author was not. BTW off topic but I've read Fischer's input consisted of allowing his name to be used to help sell the book, which is an excellent beginners book BTW.

When I give kids hundreds of tactics problems and they still open with 1.h4, I suspect that some opening instruction might be needed.

Of course tactics are essential to improvement, but they are not sufficient to cause a person to reach +1800. Just ask any of the numerous students of Michael de la Maza who faithfully followed his tactics course and never rose above 1500 USCF.
Chess requires an understanding of how to create the tactical positions, not just the ability to solve tactical puzzles.

IMHO it's easily possible to make Class-A (USCF) and higher by concentrating on tactics. Again, IMHO I think that at least some if not most players with strong tactical ability will pick up some positional knowledge along the way even if most of it is picked up unintentionally. For instance, I think that strong tacticians will eventually become aware of some positional considerations such as weak pawns, open files, backrank weaknesses, etc. AND a lot of this boils down to semantics - again IMHO - for instance is being ahead or behind in development strictly a tactical consideration? What about proper piece placement and the pros and cons of offering or defending gambits? I'm not so sure there isn't a large gray area instead of an exact boundary where tactics end and positional chess begins.
On the other hand I'm sure it's better to study positional factors in addition to tactics, although I'm not sure if concentrating mostly (not exclusively) on tactics would be a gross blunder for Class-B and lower players as a means of improvement.
This is one topic in which people who are knowledgable about how students in general (and not just chessplayers) learn things and what study methods are most/least effective might have a lot to add - even if they don't play chess at all although that would certainly help to make their input more valuable if they did. For instance, the 2 co-authors of "Bobby Fischer Teaches Chess" were experts in programmed instruction, although one was also a chess master but the other co-author was not. BTW off topic but I've read Fischer's input consisted of allowing his name to be used to help sell the book, which is an excellent beginners book BTW.
It's a fantastic beginners book, but perhaps I'm biased as it was my second chess book, shortly after Fischer won the WC when I was 9. (My first chess book was ES Lowe's "Chess in 30 Minutes"). I just recommended it to a co-worker with whom I went to lunch to give a few chess tips to.
A friend of mine had Chess in 30 Minutes. That was my introduction to chess books (mid-1970s). I went to the library and checked out one or two or three. One of them sticks in my memory: Irving Chernev, The 1000 Best Short Games of Chess (see http://chessskill.blogspot.com/2012/03/my-first-chess-book.html)

I think you need the hands on experience. It's like studying a driver's manuel for a car or reading someone's written directions on how to drive a car. But unless you actually try it yourself, you can't learn!
It is important to develop your tactical skill, your thinking skill, that is right.
So tactics are important. But if you are specialised in tactics, (So you almost ignore strategy) then a player with good strategical skill will outplay you easily. You won't find always tactics, and in closed positions usually there is not.

At what point does deep tactical thinking become positional stratagy. Something that just occured to me is I absolutely abhor giving up material even a single pawn I work vigorously to defend. This essentially means I am not playing or attempting to gambit material. How do you work on this area other then the obvious to start calculations in game on offering it. Any suggestions?
John Coffey says this, "Absolutely".
He also says, "There are other parts of the game that players need to study, but for almost everybody below 1800, tactics is their biggest weakness and the easiest thing to improve!"
He goes on to say, "I think that it is important to study tactics every day. The only exception to this might be the days where you play 3 hours or more of speed chess, because speed chess challenges us to think tactically."
Do you agree?
I'm not so sure if I do. Don't Class A players also need to know a lot about chess strategy?
The entire article can be found here: http://www.entertainmentjourney.com/tactics.htm