I agree, and that's why I think we often times put too much emphasis on statistical data as it pertains to any particular situation.
Believe it or not, I'm a believer in stats, too. I'm one of the guys who bought Bill James' original Baseball Abstract back when it was an oversized paperback and I learned a lot from it, stuff that I used in my coaching. I just believe that now we try to do too much with data and statistics.
Baseball is still a game that's played by people so the human element can't be dismissed. Professional baseball players are people and people change from day to day. A player may have had a fight with his wife that morning that affects his concentration, he may have a slight headache that he has decided to play through or he may have tweaked an ankle a bit. Not enough to keep him out of the game but enough to affect his speed or his swing just a bit. All of those things may affect his performance on the field. That affect will be minimized over a large enough sample size but it exists that day-- and that day is what's important in winning that game.
Stats are valuable in determining a player's overall value given a large enough sample size. They're also valuable when looking at splits, etc., but when trying to predict what a player will do in a "normal" situation... not so much, because 'normal' can change from day to day and situation to situation.