I didn't understand it at first either. I doubt I need to point out the obvious to you, but all of them were Noble Phantasms of some level. That shouldn't be possible.

[Waver pressed a hand to his forehead, appearing at once exhausted and in deep thought.]

...He had to have been Gilgamesh. There's no other option--not with that weapon he used. The anti-world Noble Phantasm that destroyed Ionian Hetairoi.