If someone tries to claim that they saw the Doctor in action, their account is discredited as the ravings of someone who can't differentiate between "real life" and the world of entertainment. (This is an idea which I've found is shared by my Wold Newton Universe ally, Win Scott Eckert, as mentioned in his excellent two-volume reference source "Crossovers.")
In the last few weeks as the new TV season has begun, three different TV series have referenced the Time Lord as a fictional show within their shows:
The reference to the name of "Amy Pond" could just be a coincidence; I haven't seen any evidence yet in other TV shows that his "current" adventures and Companions have been adapted for the fictional TV show.
As for the mention of TV Crossover Hall Of Fame member Russell T. Davies (League of Themselves division), RTD's televersion is most likely a member of that shadowy organization, or at least works for them in creating these cover stories.