The whole thing is a bit of a mess really and not just on a historical basis.
You can understand why there were persistent rumours after the fact that it was originally a story for the Monk and not the Master. Stuffing up established history for its own betterment is more his style, although I suppose you could argue that the Master wanted a puppet to influence Earth history with.
It's a pity that Kamelion didn't get more screen time, even if the prop didn't work because the operator died. A weak-willed shapechanger could have been interesting.