Ok, I've watched both videos now and I think the first one was cute and I really don't think it should have been cut. Yeah, she shows a lot of skin, but to me most of it looked to be her upper chest and shoulders, not her boobs proper. And the song was catchy and cute.

As for the True Mud video, I think the point of that was playing with rhyming words -- mud, spud, dud, thud. Kind of like their Law & Order parody was playing with M sounds. I'd guess that the True Blood parody is an in-joke to parents.