Well, Uriel Septim had visions because of his Dragon Blood, And Martin was able to transform into a dragon-avatar of Akatosh at the end of the main quests. That all seems a bit dragonish to me!
Again, this may have as much to do with their own natures/souls as their ancestry; I'd like to see them explained at some point, but they strike me as the kind of thing that would serve better as mystery-fodder. (Besides, it gives us something to argue about!)
Unless there's some big reveal in Skyrim; just hedging my bets, there.
Edit: it just occurred to me (bit slow today) that their talents may have derived from the role they fulfilled: they weren't descended from Tiber, but they were heirs to his throne, and each the subject of intense attention (arguably moreso than your average continent-dominating monarch). In a world where the mythic-defining-reality is business as usual, that's the simplest explanation I can reach.