Pete's World didn't have a Doctor. I'd always considered that it used to have (the Peter Cushing version of The First Doctor) but somewhere along the line one of his regenerations failed.
Doubling back to this topic for a moment, I just remembered another piece of evidence aside from RTD's BTS comment about the main universe being the only one with Time Lords: In "The Time of the Doctor," the Time Lords used the Doctor's name as a call-and-response to know if they were returning to the right universe. If they thought there were parallel Doctors and parallel Time-Lords in other universes, that wouldn't have worked. Of course, the Time Lords can be (and frequently are) wrong.
God I hate that. The Doctor memories make him who he/she is and not too mention The Doctor has been playing around with history for so long this would of come up. It would be needless re-write of the core of the show for nothing but shock value and would be the most divisive thing ever to occur for the fandom IMO.
Well, this is a blast from the past. I remember back starting around season two or three, and possibly up to the 50th, there was always a rumor going around that there was a Total Continuity Reboot around the corner, and some episode would end with the incumbent Doctor becoming either a "new" First Doctor with no history, or being revealed to be a younger version of Hartnell's Doctor.
I don't really like the idea of a dozen-or-so female proto-Doctors, if only because it seems like a cheap solution to the representation issue (see, now there are Doctors of all ethnicities and genders, so we can cast all the white dudes we want with a clear conscience), Masterplan-style mystery-driven storytelling that's frequently disappointing, and, yeah, wikipedian-trolling having us all figure out how the Doctor got two TARDISes with a busted chameleon circuit that locked on the same model, or who the little boy from "Listen" was, or what does this do to Susan, and why did no one notice another set of Doctors around history (though that's always been an issue with the potentially-infinite number of future-Doctors, and the War Doctor being referenced by River even though she wasn't in the Time War), and on and on.
On the other hand, there is something interesting about Ruth being from a more conservative era of Gallifrey. Gat was repulsed by the notion of two versions of the same Time Lord standing side-by-side, suggesting she was from before "The Three Doctors" when the Time Lords themselves broke the seal on that particular taboo, but even Ruth thought it would be dangerous for the same TARDIS at different points in its history to get too close (which could be ignorance or received wisdom, or it could be that the "shields" that were down in "Time Crash" haven't been invented yet, so the universe being compressed down to the size of Belgium is an everyday concern for Time Lords). Sure, it's a little "Enterprise," where the past of the future is mostly different cosmetically, but I'm a sucker for world-building.