Ishgard history question (pre 57 spoilers)

[Timat]

This was shown in the echo flashback after the aery.

Of the twelve, four died. One became the founder of 'The Forgotten Knight' as he and three others walked away from the whole messy betrayal, stating they had sworn to follow Haldreth, the son of Thoradan, and not Ishgardian as a whole. This left the four Knights of the four great houses to be stewards of the empty throne. Haldreth was the first dragoon, it seems, or maybe Thoradan was. He chose to abticate the throne, seemingly because of the betrayal the elzen committed against the dragons.

Ok but I still dont get how EVERY ishgardian is now of one of the twelve knights bloodline? As that makes it seems there were a few ishgardians that were not of the twelve knights that could have easily have had children and such.

[Kauthryn]

Ok but I still dont get how EVERY ishgardian is now of one of the twelve knights bloodline? As that makes it seems there were a few ishgardians that were not of the twelve knights that could have easily have had children and such.

As I understood it, and I could be wrong, the fact that Nidhogg was able to turn the fallen into dragons was proof that they had the blood of the twelve knights in them?
This was so revolutionary not only because it meant they all carried that sin with them, but that the concept of these noble families was false as everyone shared that blood.