6 months ago:
I agree there's no direct parallels, I will give you that... and for the exact same reason I would say that your pop quiz question saying House Stark = House York is not right and unfair.
I can't think of any other way House Stark is based on House York despite the fact that they come from the North. During Robert's Rebellion house Stark wasn't the only house marching on King's Landing (Arryn, Baratheon etc. marched too) and Stark didn't even end up on the throne, Baratheon did. Looking at the war of the roses, many great houses wished to see an end to the mad king's reign (such as Warwick)... but house York ended up on the throne just like house Baratheon.
And the family members? I'm not a historian but I've read several books about the war of the roses and I fail to see which family members of House York would be which family members in House Stark. I cannot say the same for house Baratheon where there are three brothers fighting each other, just like the "Three Suns of York" fought against each other.