^ Fugitive of the Judoon, The Timeless Children, the entirety of Flux, and The Power of the Doctor clearly establish within their own narratives that The Fugitive Doctor is pre-Hartnell, in turn establishing and reinforcing the fact that the explanation that every Doctor from Hartnell on gives for the TARDIS' appearance is the truth only insofar as they are aware of their own history but is not in fact the truth at all since it is established in Fugitive of the Judoon that the TARDIS did in fact appear as a police box long before the events of An Unearthly Child.
None of those episodes establish ANYTHING about The Fugitive Doctor being Pre-Hartnell. Just because we're "finding out" about previous incarnations and The Fugitive Doctor (TFD) makes an appearance or two is NOT a direct line to the conclusion that TFD is Pre-Hartnell.
Sorry, Hartnell's Doctor landed the TARDIS is 1963 and it took a local form and broke. Any Pre-Hartnell Doctor (except thru telepathy) would not know the phone box was the TARDIS.
The Phone Booth TARDIS has been traveling all around time. It's NOT established that the TARDIS appeared as a police box owned by anyone but Hartnell and the 14 Doctors since him.
That's all "viewers" backstory. Never shown/said. The production team just used the phone booth for TFD for ease (and maybe laziness) or the continuity department or Chibliss didn't care