On that note, isn't parody protected under fair use? I don't think they can send cease and desist orders (with any legal backing) on such a thing.
Really, if the artist is pursuing people legally than woot wants to play it safe here.
However, being a long time fan of Weird Al, I've picked up a few things on parody over the years. Weird Al usually contacts the people that he is parodying and asks for permission before doing his humourous take on them. Most say yes, some are jerks and claim they never said yes then take it back when they are found to have no sense of humour, and one (Prince) consistantly turns him down. That being said, parody artists do not need to ask permission to do parody, it is in fact, protected legally.
All that said though, I can understand why woot would reject. If the original artist is really uptight, then even if they have no ground to stand on, why would woot want to entangle itself in a possible legal battle?