I guess I'm not being very clear... bit of a tough one to describe...
The audience will definitely see a stick go flying off into the bassist's eye, I completely agree, but from a personal point of view I find being in that situation forces me to work within limitations while I scrabble around for another stick... often it produces interesting results, especially if the rest of the band pick up on it and start playing differently to accommodate - you can end up in some cool weird loops all because something happened that wasn't meant to. These days I just don't care about the audience spotting mistakes, because hopefully they'll also spot the fact that I adapt my playing to keep some kind of flow and coherence. Just for the record, this isn't to say that my playing's riddled with mistakes either, this rarely actually occurs but I like to be prepared mentally for anything that may (or may not) happen.
Of course, it might just look rubbish and perhaps I'm talking crap, but for me it keeps things open and interesting.
What I'm really not saying is "just learn to deal with your mistakes", please don't think I am, I just like to keep my approach to drumming fresh and organic at all times.
Am I making any sense yet?