Read "The Book of the Dragonborn" it pretty explicitly lays out what the dragonborn are. They are mortals with the souls of Dragons, who are thus able to devour the souls of other dragons.
And you can't see the all the problems with that book? It outlines the concept that being Dragon Born is something divinely granted, practically hereditary but only when convenient.
Then there are phrases like:
"The line of Septims have all been Dragonborn, of course, which is one reason the simplistic notion of it being hereditary has become so commonplace." There is no bloody unbroken line of Septims. It's the primary argument against the hereditary nature of who gets to wear the Amulet of Kings.
Or little gems like:
"Those who become Emperor and light the Dragonfires are surely Dragonborn - the proof is in the wearing of the Amulet and the lighting of the Fires. But were they Dragonborn and thus able to do these things - or was the doing the sign of the blessing of Akatosh descending upon them? All that we can say is that it is both, and neither - a divine mystery." When we've seen Mankar Camoran wearing the Amulet of Kings. Nevermind that the bloody AoK is an Ayleid artifact.
Now I'm not questioning that there are indeed people who are able to absorb the souls of Dragons. I question the blanket assumption that every emperor has been one.
Again, my main point of contention with the Arcturan Heresy are that Tiber Septim (not Wulfharth) went to High Hrothgar and WITHSTOOD the power of the Greybeards thu'um. Arngeir EXPLICITLY tells your character this in TESV. Still, the idea that Wulfharth was a Shorine and was only confusedly known as Ysmir due to HEARING the prophecy from the Greybeards (but not withstanding their voices) is an interesting one, well worth consideration. But, even if true, I still maintain that Hjalti Early-Beard was dragonborn, who learned of his destiny from the Greybeards and also studied the voice with them. The Heresy mention Hjalti AFTER Wulfharth visits them, so Hjalti could easily have spent a few years learning the voice and THEN gone off to fight for Cuhlecain. His learning the thu'um under the Greybeards and serving under Emperor Zero are not at all mutually exclusive.
The story you tell is found in the first PGE.
The Song of Tiber Septimhttp://www.imperial-library.info/content/pocket-guide-empire-first-edition-cyrodiil#5
From the Odes:
"He was born in Atmora as Talos, 'Stormcrown' in the language of the ancient Ehlnofey, and it was from that shore he sailed. He spent his youth in Skyrim among the Nords. There he learned much from the Tongues and their chieftains and their ways of war. At twenty he led the invasion of Old Hrol'dan, taking it back from the Witchmen of High Rock and their kinsmen.
"Soon the Greybeards made known that they were restless. Already the storms had begun from their murmurs. The Greybeards were going to Speak. The surrounding villages were abandoned as the people fled the coming blast.
"The villagers warned Talos to turn back, for he was marching to the mountain where the Greybeards dwelt.
"Inside he went, and on seeing him they removed their gags. When they spoke his name the World shook.
"The Tongues of Skyrim told the son of Atmora that he had come to rule Tamriel and that he must travel south to do so.
"And it is true that Talos did come to Cyrodiil shortly after the Battle of Old Hrol'dan.
"And it is true that a great storm preceded his arrival."
Which is what the whole Heresy started with.