^I wouldn't expect a Star Trek/Doctor Who crossover to be in continuity with either series, so I don't see why that would be a consideration.
Because Star Trek exists as fiction in the Doctor's universe? A fair point, I grant, but there are other precedents for this kind of thing in past crossover fiction. For example, DC Comics characters exist as fiction in the Marvel Comics reality, but that hasn't stopped multiple stories where heroes from both universes meet one another. Heck, according to some writers, aspects of Trek exist as fiction in its own universe, via the writings of Benny Russell!