We caught modern genital warts because our ancestors were banging Neanderthals
Nothing like this story as been such a race to the bottom for headlines for a long time.
I will note that Annalee Newitz has a much better version of the story with this winning quote:
[A]lways practice safer sex, even if you're getting down with a Denisovan.
There is, by the way, the interesting question of whether Neandertal immune variants might influence susceptibility to the strain in question, which has made little inroad into sub-Saharan Africa.