Silman didn't say to play blindly. If you read the chapter in HTRYC on his thinking technique he explicitly states after finding a candidate move to ask youself, "Does this move have any tactical refutations?".
Edit: It is actually in the chapter on Calculation (which is looking into your candidate moves...). Page 40.
I am surprised that Silman's middlegame books get good reviews, because in my opinion they are deeply flawed. Below is my Amazon review of Silman's Amateur's Mind. Do you agree/disagree?
The Amateur's Mind teaches the reader to use the following thinking technique during a game of chess:
1) Do not look at individual moves!
2) Look at the imbalances (strategic factors, such as outposts) in the position.
3) Create a plan based on these imbalances. Now you may look at individual moves.
The problem is, this doesn't work!
If you try to do this in a game (and Silman suggests doing this every move) then you will blunder, over and over, because you will not notice the tactical possibilities in a position. You will get mated in three moves, or you will allow your opponent to win material with a simple knight fork.
You need to look at individual moves first and foremost. Tactics comes first; strategy second. This is self-evident to any decent chess player --- but not to Silman, who believes that strategy must come first. I would actually go so far as to say that Silman advises you to mostly ignore tactics!
For this reason, I cannot believe that The Amateur's Mind and How To Reassess Your Chess have such good reviews all over the Internet. I am sure that people who rate these books are simply disregarding Silman's "thinking technique" advice. But this is the central idea of both books.