Clock recovery over HDMI is complicated. The audio data's packetised and sent in bursts, in between video lines. It's up to the receiver to do a good job of clock recovery - in theory it could do it quite badly. But it could also do it perfectly.
I wouldn't say that HDMI is inherently inferior on that score. But in practice, HDMI seems to cause problems in all sorts of areas by being complicated. There's lots of scope for errors and incompatibilities.
48kHz vs 96kHz for HDMI would have nothing to do with jitter. It couldn't affect anything like that, at least for HDMI.
I repeat what I said elsewhere - if the data is 48kHz on disc, the player should by default be outputting it at 48kHz. It shouldn't be attempting to "improve" the data. In HDMI output mode, it should be functioning pretty much as a plain transport, like a DVD or CD player with S/PDIF.
Outputting at higher rates can cause problems - some receivers can't handle 96kHz signals as well as 48kHz signals (fewer processing options function).