You're right, of course, the two notions are orthogonal, but in practice an open-source project like Mozilla cannot use royalty-encumbered codecs.

As for the royalty-free nature of AV1, it will only be known once all the patent lawsuits are litigated. The AOM patent litigation fund in itself is no guarantee, given the capricious nature of common-law courts.

I think the specifics matter here and I'm not in any way versed well enough in law to know so correct me if if I'm wrong but:

Mozilla could absolutely use and distribute x265 but that would also require them to have a license for the patents required for HVEC and would also require the users to have a license (which is of course unrealistic).

The only reason firefox can play h264 is because Cisco paid for an unlimited license with subdistribution and assigned it to mozilla.

So as h265/HVEC is concerned the problem for mozilla is that even if someone wanted to pay the bill like cisco did they would not be able to get a straight answer who and what they needed to pay for a license, right?

That's exactly right. While it is impossible to absolutely prove a negative (that no one will make a credible patent claim against AV1) -- it's worth noting that the line of codecs starting with VP3 that led up to AV1 go back to research done in the early 90's, and there has never been a serious patent claim against any of them.

This is at least partly by design: On2 had an explicit mission to create competitive codecs that avoided conflict with the MPEG patents. I'm pretty sure this was a major factor in their appeal to Google.

(Disclaimer: I was CTO &/or CEO of On2 up until 2003)