Fenrir's Fangs

Well my character did show him that he had a TARDIS, and my character knew about The Great Time War. (When the planet blew up as you put it...by the way the planet was called Gallifrey.) And the only two alien species that would know about the war would be either a Timelord or a Dalek, and my character is obviously not a Dalek.

Also The Doctor has accepted the idea of other people being Timelords with very little proof being provided. One example would be:

In the movie "The Next Doctor" The Doctor is convinced that a man is a future incarnation of himself simply because the guy acts like The Doctor.

Sometimes The Doctor can be pretty easy to convince I suppose...besides he's been led to believe that he's  the last of his kind all this time he's probably eager to believe he's not really alone.