I always think that whenever we complete job quests and get new skills, when the text says something like "crystal resonates" that means the soul crystal bestows upon us skills of old i.e skills that have been discovered by the soul crystal's previous owner and been recorded inside the crystal. BoTD and its related skills fall on this category so I believe that the skills are quite common among high level dragoons.
Blood of The Dragon in my opinion, is tapping into the the power of dragon inside, which actually makes sense if Ishgardian dragoons can do that because
Every Ishgardian has Ratatoskr's blood in them.
As to why WoL can use BoTD, I never notice it implied it's because of our link with Midgo though of course I may have missed it, but isn't it possible that somehow somewhere, we have dragon as ancestor? Or maybe someone in our line committed the same crime Thordan I and his knights did?