Unless Susan's memory was wiped also? The Doctor was working for Division a long time. Let's suppose that eventually Division decided to retire the Doctor. They forced a regeneration on Jo Martin's Doctor (or maybe the one that came after her) turning her into Hartnell, who'd had his memory wiped/tinkered with to make him believe he was the first incarnation. Now maybe Susan was the Doctor's final companion of the Division era, and the Doctor insisted that any deal involved her too. Maybe she wasn't even a she, maybe a male Timelord was regenerated into Susan, possibly as a young child, and given false memories to match the Doctor. Does it sound far fetched? Maybe, but Tennant, Yana and Martin all thought they were human and had detailed memories to match so it's clearly not beyond Timelord technology. For me the sticking point (aside from the Tardis as a police box which can be explained away) is how the wider Timelord society wouldn't have been aware of the Doctor's previous life working for Division? Unless it so was hush hush that very few people know she existed? Whether Hartnell was a recent regeneration and Susan a former companion, or whether Hartnell began life as a young man and grew up, married and had kids who had a daughter etc hardly matters. Presumably at some point the niggling concerns that had been at the back of his mind his whole life, that something wasn't quite right, that he didn't know all he should know about himself, that some memories seemed a trifle thin, prompted him to run, and whether she was his actual granddaughter or not, both he and Susan believed she was so she went along with him.