>I am not aware of any mysteries that are most simply explained by a hitherto unobserved, technologically advanced (I assume we're not talking about dolphins when we say) "non-human intelligence"

This is precisely the point. You aren't aware of these mysteries, despite the earnest attempts of many to bring them to your direct attention.

There is no longer any attempt to hide the mysteries categorically, so this lack of information is now on you.

>I am not making a truth claim here, as in "it's definitively untrue that there are non-human intelligences sharing the planet with us," I'm just arguing that it's an extraordinary claim that should require extraordinary evidence - grainy footage and hearsay isn't enough for me.

Yes, that's why the correct scenario is wide declassification of the premises that are asserted in this regard, i.e. to make general knowledge of unidentifiable phenomena which have no definitive known cause or origin, communication with these entities, capture of their technology, etc. All of these things could be explained by various competing theories, some of them "simple" (funny how Occam's razor is always just what I prefer), but this information, which has been trickling out from credible sources, needs to be brought into the public space and then we get to decide what it implies or doesn't imply.

Right now there is a deliberate veil of secrecy and serious mysteries that aren't denied by anybody serious. They definitively exist.