The way I "fact-check" a celebrity Twitter is to see who they are - or who they're not - following. Sure, you'll get the celebrities who don't follow anyone, but the release of their Twitter name is through unmistakably official sources, like their homepage, people they know and/or work(ed) with, etc. I also check their and their friend's histories - if it's official, 95% of the time, someone they know will make it public (case in point: Peter Davison. He doesn't have a verified account, but the editor of Doctor Who Magazine and Project MotorMouth vouched for his account), and they'll probably have a verified account themselves.

If you think Doctor Who has a problem with fake accounts...you don't know the world of football (Soccer, Americans). So...many...parody/fake accounts....