A note on the Doctor's age

Steven Moffat says the Doctor can't possibly know how old he is, which is why, despite what is said in the old series, he decided that the Doctor was 907 as of Vampires in Venice, even though he said in Time and the Rani (Seventh Doctor) that he was 953. And that's if you're just taking the show as canon (which I am). If you accept spinoffs and alternate media, though, he's established that he's over 1100. Of course, there is evidence that he does lie about his age. But that's not what Moffat says. He says he couldn't know how old he really was unless he was counting on the wall or something. Couldn't the TARDIS keep count? He travels in time with the TARDIS, so presumably their timelines are pretty much in sync. Another theory (supported by some spinoff media) is that he adjusts the number based on the length of a year in the context in which he finds himself. I think it's silly. He may not know exactly, but even at around 1000 years old, 100 or more years is still a big difference, right? When you're 90, maybe you would have forgotten exactly how old you are if not for people reminding you, but you know you're not, like, 78, right? I mean that's still a big difference, right? Percentage-wise?