Well, it turns out there was a really good reason that the Brigadier could assert that solid objects didn’t just dematerialize.
He doesn’t remember the Doctor.
We see the Doctor inadvertently save his own life, avoiding Turlough dropping a rock on his head, by fiddling with a device that handily explodes and knocks both men on their ass. Then the Brigadier shows up and, as I said, doesn’t remember the Doctor. And not because the Doctor regenerated at some point after their previous meeting. No, he has no idea what the TARDIS is or who the Doctor might be. He remembers UNIT, but that’s classified.
He is polite enough to take the Doctor back to his house to talk things over, and his memory returns once the Doctor starts naming their old associates, especially various female companions, and we get a flashback of the Brigadier remembering all the previous Doctors from old episodes.
Did he ever meet the First Doctor? I mean, they showed a clip from the tenth anniversary, but I think the question stands.
Point is, he remembers now. Can he help the Doctor find the TARDIS?
Well, he may not have to. See, the Brigadier also met Tegan.
The Doctor is talking to him in 1983.
See, the TARDIS did materialize near the Doctor, but then it vanished again. It did reappear near the same school, but a few years earlier, and when the transmat pod appeared with a barbecued guy inside, Tegan and Nyssa assumed the injured man was the Doctor, and said man didn’t correct the women. When Tegan went for help, she found the Brigadier, and he did remember the TARDIS and the Doctor then. The two head back to the TARDIS to see the burnt man seems to be…well, not the Doctor. He’s sort of healed, but also his head seems to be missing the top of his skull.
So, the Doctor needs to get back to the TARDIS or the TARDIS needs to find him sometimes in the next five years. Something made the Brigadier forget all about the Doctor in-between. And Turlough decided the Doctor is good and doesn’t want to kill him. Too bad the Black Guardian insists the Doctor must die anyway because to the Black Guardian, good is evil.
I’ll give the Black Guardian this much: at least he’s honest. Eventually.