Ha, I thought it already had been! I think these websites can be awfully hair-triggered when it comes to takedown requests, sadly. You can basically email them claiming to be the owner of any video and they'll remove it just in case.
Everyone is very twitchy about getting sued these days. Look at the recent incident of a young lad called Rooney who couldn't get his name iced on an Easter egg at Thortons in case Wayne or ManU sued. Whether any mother should call a child Rooney is a separate issue
You could easily shame them into dropping it. The tabloids would be all over it. A picture of a sad looking child with a blank cake, and a sensationalist headline.