Never been a fan of "balance for the sake of balance"; if they can't stop you running the football, no need to throw it 15 times. If you can't get but 1-2 yds per rush, you better throw it more than 15 times. Do whatever you have to in order to win.
I don't have any stats to back this up, but I would bet at least 25% - 35% of all interceptions are the result of deflections by the intended receiver - bouncing off of hands, helmets, shoulder pads, etc. Anytime you hand the ball (or lateral) from one person to another the chance of a fumble is doubled, I would say.
Three things can happen when you throw the football, and two of 'em ain't good. Didn't somebody famous say that?
IMO, when it gets down to it, if no one drops a ball that hits their hands, from either a pass or a lateral or a handoff, there will still be fumbles and interceptions - just not as many.