I encourage you to take your own advice and chill, because reading attacks into something where there are none is a definitive sign of being overly stressed by a subject, or in this case, by people pointing out flaws in things you like.
It's not "a little different".
If Hydaelyn says that the "crystal's former bearer" said something, then that means the person who previously owned it -> Emet-Selch, since Azem never owned the crystal (until the WoL received it, technically)
If Hydaelyn says that the "creator of the magic" said something, then that means the person who created the magic that was copypasted into the crystal -> Azem, the summoning magic was their thing
And I will also tell you why the first option is wrong: Why on Zodiark's green earth would Emet-Selch say anything about how Azem's summoning magic works in detail? He has better things to do than spilling trade secrets without consent.