One popular rationalization in continuity discourse since The Brain of Morbius for the Doctor's extra faces was that those were actually Morbius' faces (the Doctor's dialog in the previous panel alludes to this interpretation), which could be argued from the way the scene is edited, but is inconsistent with Sarah Jane's reactions while watching them.

Another popular rationale was that the Doctor had a previous regeneration cycle; however the incarnation first appearing in Doctor Who, the first incarnation of the second cycle, would remain "the first Doctor" (e.g., The Three Doctors, 1973) because it was upon being granted a second regeneration cycle that the Doctor adopted the title to the exclusion of his given name.

The wraparound idea was originated by Naomi Pardue in the 1980s. The extrapolation corrolary was my contribution to it. Here, I don't know where the Doctor is just saying that to have something to tell Sarah.