I wonder would this also explain how Three knew (in The Five Doctors) that his successor was “all teeth and curls”? Some have speculated that the two had an offscreen team-up adventure but usually the earlier incarnation doesn’t remember anything about his successor.
I thought Sarah was doing the grin and hair twirling motions that got 3 to say "all teeth and curls"?
I do recall 2 saying to the apparitions of Jamie and Zoe that they shouldn't know about him (but the Time Lords didn't erase their memories completely; only all except their initial meeting of him.)