Actually, eBay does it all the time.

When a company contacts eBay to complain about an auction, eBay almost always sides with the company. Cases I'm familiar with:

1. I had an extra copy of Microsoft Windows - shrink-wrapped from the store. However, I had removed the UPC code to get a rebate, so I couldn't return it. When I listed it on eBay, Microsoft objected (their shrink-wrapped agreement says you can't resell the software) and eBay took it down. The fact that it was authentic and in the original packaging didn't mean a thing.

2. I had some Maui Jim sunglasses that I received as a promotion, but didn't want them so I listed them on eBay. To illustrate the glasses, I used a picture of the glasses from Maui Jim's web site. Maui Jim complained about my use of the picture and eBay took the auction down.

3. Several times I was bidding on something (I can't remember what it was), and received a notice from eBay that the auction was being ended for some reason related to intellectual property.

eBay most certainly can take this auction down and if AA complains, they almost certainly will do so.