Let's not forget that Summoner was
invented by the Allag - people who practically worshiped their own dominance of Bahamut. Draconic likenesses are hidden
all over their gear (not so hidden on the dreadwyrm but I can't even figure out if we're supposed to think that they wore that or if it was "aetherially created" a la Louisoix and Nael's new frames). Look at the
summoner horn -
even it is suspiciously similar to Bahamut. One big central horn, two smaller horns to the sides of it, triangular pieces over the ears. With Bahamut's essence returned to the aether (and he's the size of a city - that's a lot of formerly-of-Bahamut aether), one need not necessarily have cleared Coil to be able to channel his power; something could just as easily come up in the job quests (though, as others have said, we now know that the storyline is canon by patch -
you in the story finished the Coil in 2.4, even if
you the human didn't clear it yet.