This is more of a 'book' theory, but has no material impact plus fits just as well with the show and falls into the interesting secret backstory category: What if the Mad King was right to be paranoid about the Starks?
Now we're lacking a lot of information, but prior to Robert's rebellion you there doesn't seem to be a lot of co-mingling among the great houses. If they were intermarrying you'd have something like the eventual European dynasty's where all the royalty were eventually related. Yet if that's the case here's Lord Rickard Stark in short order using his children to bind house Baratheon, Aryn, and Tully to the Starks. You have to think that once they lost their dragons it was only a matter of time before someone took a run at the Targaryan's, and that's a huge block of power.
Why did King Aerys summon Rickard and Brandon Stark to Kings Landing and burn them alive? Sure he was mad but that above probably had everything to do with it.