Physical pain is part of football, everyone gets that. However, if a player is physically harmed by something that isn't within the context of football or relevant punishments (ie, being burned), I don't think that is ok. I don't care if he had to do 1,000 pushups or got put in the middle of a tackle circle for 10 minutes, or anything along those lines, I don't even care if he had to bear crawl across the field, but if he has to do it in a situation like this, where it is going to physicall harm him in a way that is unintended, then you need to find something else.
With that being said, Mangino may have been a good coach, but he didn't seem like a quality human being (only from what little I know), so I can't say it was a bad decision.