I don't think it's any of that. For my test I quickly ran through g end and then to carrol river (only defeated jack). I did talk to cheshire in the prison and so did they. I say straight to dlc 3 but they did go around getting covenants while I didn't do that in my test and cheshire was there for me. Cheshire ring also carries over in ng+ so I don't think that's it.
That seems to boil down to a very specific thing.
I thought about the Cat Ring because of the interaction you have with her. You already said it isnt related to her boss encounter & you + video person got her scene in the dungeon.
The game remembers previous endings you obtained. But thats kinda a huge task to check.
There is always the possibility of a version difference/bug but then again BS2 has tons of minor triggers/event flags.
If it isnt directly related to Chesire as a NPC & it isnt her ring either. 2 Train of thoughts:
-It remembers something from previous loops/endings? (But unlikely that ABC would be tied to this. As you already pointed that out)
-Is it more technically tied to some sort of interaction roadmap. NPCs progess when you rest at bornfires in a new area, bosses defeated or that one thing in the snake church.
Could it be that their Chesire simply is "stuck" somewhere in the main route of the game? If said person from the video unlocked some convenants & Chesire appeared on the newest/latest bornfire.
I vaguely remember Chesire cant be seen in certain SEN values. The instance i remember was Mad Hatters Tea Party. Where Chesire appears/disappears on that one tree. But that also seems very unlikely.