Not to be rude, but the Master (an in-universe character)'s word is better than yours. If you are to throw doubt on what the Master says because "he may be lying", when no reference to that ever came up in the show, what is to stop me from discrediting every last detail as a character "could be lying"?
If push comes to shove the Timeless Children will also have to end up in the ambiguous section, they and the Morbius Doctors were intentionally placed among a montage of confirmed Doctors. While the Other exists in complete obscurity.