I don't understand how this affects mom and dad, really? Ok, so he's having accidents at home. They can deal with that how they choose. But if he is not having accidents at your home, then I would say what's the big issue with him being "potty trained" at your house?
I agree that it sounds like he is using this as a control issue at home!!
I don't think I would feel comfortable saying, "Too bad, I am going to keep doing what I think is best." or fibbing to the parents about what you are doing. I think you have to let mom and dad know what you are thinking, including "I find it difficult and un-necessary to change his poopy diapers when I know that he is willing and able to use the potty."
And I find that parents often switch to pull-ups waaaaaay too soon, so yes, the child believes that they are just a new kind of diaper. We made wearing a pull-up a reward in itself, and used the same "Don't pee on Diego/Dora!" tactic. Pull ups are for AFTER the child has had experience using the potty, and has shown some success doing so.