That was what he wanted people to think, yes, and he did marry a princess of the house of York, but even if he had any York ancestry at all (which a quick Wikipedia check seems to deny, but I too seem to recall having heard it), it was clear that he was the leader of the Lancaster party, re-invading the country after York had clearly won the prior stage of the war and taken control of the entire country.

It's interesting, too, that Tudor's claim to Lancastrian ancestry was actually based on descent from an illegitimate Lancaster scion, who was retroactively declared legitimate after his father finally married his mother, when the son was 22 (!).

Anyway, yeah, those parallels don't go very far. The part about the mad king's child (or grandchild, as the case may be) having its brains smashed out against a wall after the violent deposition of the mad king is straight out of Suetonius, on the other hand (I just finished I, Claudius, which is little more than a calque of Suetonius, so contained that story as well). Although I'm not entirely sure if that's come up in book one already or not.