I'm still trying to process how Ruth can be the Doctor, I'm thinking it has to be a parallel universe that has somehow over lapped and that is why neither has any knowledge of the other.
There is an old fan theory that could explain it.
Basically, the theory goes that when the Time Lords caught up with the Second Doctor at the end of The War Games, then instead of immediately forcing him to regenerate into the Third Doctor, they instead co-opted him into working for the Celestial Intervention Agency, which is the Time Lords' black-ops squad.
In this scenario, Ruth would be an additional regeneration between the Second and Third Doctors. In some ways that fits what Ruth says about having a job she didn't want and why she's on the run after quitting said job. The reason Thirteen doesn't remember her is that presumably the Agency caught up with Ruth at some point, wiped her memory of her time at the Agency and regenerated her into the Third Doctor. The reason Ruth doesn't remember Thirteen is that Thirteen is Ruth's future, which I think is what Ruth says in the episode.
The theory has semi-canonical status in that there are a couple of novels and audio plays which take the idea and run with it, although the Doctor in those is the Second Doctor. It's also how a lot of fans explain The Two Doctors, the Colin Baker serial where the Second Doctor appears to be working for the Time Lords. The theory has a couple of problems, not least that the Doctor would have run out of regenerations at the end of the Tenth Doctor's run, rather than at the end of Eleven's time. But I'm sure a suitably hand-wavy explanation could be produced to get around the inconsistencies. After all, what's one more retcon at this stage of the game.
I heard the Ruth Doctor may be pre the First Doctor and the Doctor's mind has been wiped of earlier regenerations. This would be a belated attempt to explain the Brain of Morbius.
The problem with the pre-Hartnell theory is that the exterior of Ruth's Tardis is shown to be a police box. However, the Tardis only got stuck as a police box after it left Totters Yard at the end of the very first episode. Prior to that it wasn't stuck, a point which I think Susan makes in the first episode.
