Mike Patton loves pop music. Those covers were most likely not mocking anything. I love me some Faith No More but haven't heard them cover Nothing Compares 2 U (which is actually a Prince tune). I'll have to check it out.
EDIT: You weren't kidding. I can't find a cover of it. Please! Share it!
See sibling comment:
FNM’s cover of the Commodore’s Easy is both ridiculous and sublime. Man they can play.
There was a good bbc show of theirs floating around on YouTube. The music is so intense that I feel these quieter pieces give one a chance to catch one’s breath.