From the WOIAF:
That entire snippet is poorly done from a historical perspective. I’d ignore it as completely inaccurate. It makes more sense for the Starks and Barrow Kings to have been rival petty kings rather than vassals for purely mundane reasons, not to mention all the other inaccuracies.
Thanks for the question, Anon.
SomethingLikeALawyer, Hand of the King
“Song and story tell us that the Starks of Winterfell have ruled large portions of the lands beyond the Neck for eight thousand years, styling themselves the Kings of Winter (the more ancient usage) and (in more recent centuries) the Kings in the North. Their rule was not an uncontested one. Many were the wars in which the Starks expanded their rule or were forced to win back lands that rebels had carved away. The Kings of Winter were hard men in hard times.
…More historical proof exists for the war between the Kings of Winter and the Barrow Kings to their south, who styled themselves the Kings of the First Men and claimed supremacy over all First Men everywhere, even the Starks themselves. Runic records suggest that their struggle, dubbed the Thousand Years War by the singers, was actually a series of wars that lasted closer to two hundred years than a thousand, ending when the last Barrow King bent his knee to the King of Winter, and gave him the hand of his daughter in marriage.
Even this did not give Winterfell dominion over all the North. Many other petty kings remained, ruling over realms great and small, and it would require thousands of years and many more wars before the last of them was conquered.”
In other words, you have a context of dozens of rival petty kingdoms, you have the Starks claiming the title of King of Winter from the beginning, and you have a situation in which the Barrow Kings claimed supremacy over a rival king, not a situation in which the Starks were rebellious vassals.
So whoever put together that video baldy misinterpreted this chapter in the WOIAF. Hence the idea that the Manderlys fought back the Andal invasion, despite the fact that the Manderlys didn’t leave the Reach for many centuries after the Andals arrived in the Reach, which in turn was long after the Andals had arrived in the Vale, the Riverlands, and the Stormlands.