I think I've stated a few times on here that I'm not a stats guy, but not because I don't respect stats. I just don't have a good mind (or perhaps simply a lack of desire to have a good mind) for stats. Also, even avid stats gurus will remind you that no one measure of a player or team is ideal in a vacuum. So here's one person's argument against over-relying on stats as a measure of a player's worth.
Every single thing that happens on the court is impacted in some way by everyone else on it. There are assists created by a point guard’s brilliant dribble and those created by off-ball movement. There are rebounds where a player soars between two opponents, and those in which a player grabs his own offensive board on a fast break. Players are wide open at times, and defended extremely well at others. The shot clock is always a consideration. There are literally hundreds of other factors that affect exactly how valuable a given basketball action might be. There are certainly combination stats that are preferable to PER (I am fond of basketball win shares. Google it), but there are no formulas advanced or detailed enough to measure all the variables that basketball represents. It’s for this reason that many analysts enjoy adjusted +/- as a way to figure out how a player impacted a game without having to break it down into individual pieces. But there are holes in putting your faith in +/- as well.
Again, I think most stats apologists wouldn't refute the imperfect science of numbers. They have to be taken as part of the whole analysis package. You can't just assume a guy with better rebounding stats is a better player than another player without watching him actually play basketball (not to mention accounting for the team and situation that both players played in).
Basically, I'd say that relying totally on stats is missing the forest for the trees, while dismissing stats outright is lazy and closed minded. But that's just my two cents.