Yeah, McCoy is kind of weird in this regard. Even in his peak Philly days, he would routinely carry the ball that way (he doesn't do it all the time, but he does it frequently). But when you look at his stats over a large sample, he doesn't really have a problem.
I suppose one could argue that opponents have picked up on his style and are now exploiting it, so if left unchanged we would see a dramatic increase in fumbling rate. I don't know if that's the case, but it is plausible.
I also think if you're going to assign blame, Reid deserves at least some. McCoy has always done this. It's not something new. If he felt it was a problem, then he should have addressed it by coaching him to hold it differently.