So who's right? Well, obviously, cave-people weren't going to cave-restaurants to watch dancers in bearskin bra-and-belt sets perform 5-part cabaret routines, and I don't think the "world's oldest dance" advocates are suggesting such. I think it's fair to assume that ancient fertility dances involved pelvic moves, such as circles and figure-8s, that wouldn't have been substantially different from what is found in bellydance today. And there are a few accounts from Roman times that appear to be describing other "bellydance" moves such as shimmies.
Of course, one would have to be using a very broad definition of the term "bellydance" in order to fit those ancient moves under that description. I see bellydance as being a lot like the English language - although today's English can be traced back to Old English, there have been so many alterations, additions from other languages, etc., that what we speak today would be unrecognizable to "English-speakers" in 500 A.D., and vice versa.
What would be more accurate is if dancers would tell reporters something like "Although certain moves in the dance likely date back to ancient times, bellydance as we know it originated about a century ago, when the West was introduced to the dances being performed in the East at that time. Bellydance today is a mixture of Eastern and Western influences ..." and hopefully have time to give a little bit of the dance's 20th century history.
At any rate, since I think the "world's oldest dance" line in newspaper articles is an improvement over the "lascivious dance of seduction"-type write-ups of previous decades, I won't complain too much about it.