"Think mirror" isn't a license to invoke contradictions at will. Mirrors are a reflection, not an inversion, or antithesis.
The fact of the matter is that all ancient peoples had very similar themes among them regarding their origins from gods and the designation of their leaders from dictate of the divine or as descendants of the gods.
I am not just running off with an unchecked creative license, here. If future proves past, and we are talking space and the like - then the existence of beings from the stars in our past is not exempt from the subject of Q.
Of course, UFOs are a distraction. Releasing little tidbits about rumors and sightings is a classic way to get people to engage in rampant speculation about what is "out there" while still being unable to tie it down to anything "down here."
It's a diversionary tactic even if there is truth in what is released - that the government has indexed weird things its military sees. Whether those have anything at all to do with Q's "incarnated alien" response is almost impossible to discern.
But… If you believe those who know talk using art and symbolism in fiction - then "Ugly Hood" is an interesting candidate for being such a thing.
Someone using the name Q has been a redrawer and typesetter for manga translations - and Japan knows Q.
Would it really surprise anyone?
(Granted, that is a Korean Manhua web comic… But same thing).