I think you overstepped too. Re: the fat jokes - he may be socially inappropriate, but it didn't sound like anything other than trying to get the child to laugh. Re: the "private parts" conversation - when I go to the playground, I take the opportunity occasionally to remind my daughters "what would you do if someone..." and the answer is something like, "scratch theri eyes " or "bite them." If you heard that you might have thought me inappropriate too, but I would strongly disagree with you.
Look, I am pretty uptight, and I don't like your description at all. But not sure it is bad parentling. The worst part is what was said to you / about you afterward. But they were pretty ticked off, and I might have been too. I doubt it was a real threat, just childish.