The comment I quoted there is just someone being hyperbolic.
I agree with the suggestion that some tactical practice would do some good. Try spending some time doing puzzles! They at least will reward looking at every piece on the board to see what it's doing. As a Diamond member, you can try as many puzzles as you want.
Puzzles and tactical practice don't really directly address blunders, but they do encourage greater board awareness, and you'll only have to think "Oh damn I missed that bishop/rook across the board" a few times before you start looking for bishops and rooks across the board.
If you do this, don't let the timer stress you out. Just take the time you need to figure out what you think are the best moves.
Edit: A thing that can be really great for puzzles is to go to the main Puzzles page, choose Custom Puzzles, check all themes, clear out the rating range, and from the drop-down menu labeled "include," choose "Puzzles I have failed." Then, you can JUST practice the ones you missed. If you fail them again, look at the solution, then choose Restart Puzzle and play them five or ten times over and over again. You'll find your tactics will improve.
All that said...is no one surprised at how well some of my 300-400 opponents are playing?
Part of my frustration is that I was told anyone under 600 doesn't even know how the pieces move.
Nah...they are just trying to make a point that players under a rating of 600 don't usually perform very well relative to more experienced ones.
In reality, a player who does not even know much of chess beyond the basics are likely rated under 200, considering the fact that the rating floor on this site is 100.
In this site, the rating spectrum for games varies from 100 to 3000+, with the median or average rating probably being 900. Even if you were to lose your games, they probably won't go down much. But when you do win...a whole new level of rating awaits you.
As a reasonable start, you could train up some basic tactics...or reward yourself with a chocolate for every five games you play with no more than three hanging pieces in each game. It's too much to ask for zero hanging pieces for now, but I'm sure that keeping your hanging pieces count to three or fewer in games is achievable most of the time.