Thinking about it... Yeah...
How did Garuda respond to Gaius? She had Ifrit and Titan summoned so she could feast upon their aether...
How did Ultima Weapon actually "capture" Garuda? By biting her head off... OK not the case for Ifrit and Titan, but both were pulled in front of the weapons "head", mayhaps it sucked up their dissipating aether?
Now I just need Free Company Summoning to be introduced and explained by Quina Quen, or any Qu relation, and I'm certain of it...
They really do drive home the whole "feasting" theme with Garuda though, makes me think there really is some truth to the mythos... If she gained the power of the Vortex by consuming the Lord of Snakes that could explain how he kept life land-bound (he used the power to prevent flight), though if he was a Primal he shouldn't have left a corpse behind to be feasted upon... Unless he was used by the Allag in a similar fashion to Bahamut... Preventing flight by manipulating the wind would be a useful when waging a war with dragons...