AB might have some insight to this? 
Depends where the ball is.
If it's already over his head and in the end zone, just kick it out the back of the end zone.
If it's not yet in the end zone, our punters go through a 4 step process in evaluating what to do:
1. If you can still punt it, punt it.
2. If you see an eligible receiver, pass it, perferably incomplete. At least the ball is returned to the LOS.
3. If there is no receiver, run with it.
4. If all else fails, fall on it.
I say our punters go through a 4 step evaluation process. In reality, these are 17 and 18 year old kids trying to make a decision when all h#ll just broke loose. You hope they remember the steps, or at a minimum, don't let the defense pick it up. Even falling on it inside the 10 beats letting the defense picking it up and running it in for a TD. Live to fight one more play.
As for punters getting creamed, once the snap goes over the punter's head, that's pretty much a given.