Unless my understanding is completely wrong, I would have to say that Factions really don't affect door locks for players in any way, shape or form. I'm glad it fixed your other issues though - that is the important thing!
I am sure you know much more about this than I do, but my experimentations have shown that doors and factions are wonkey, at least in my game. I have a door that connects 2 interior cells. when I set a faction on the door, and lock it, and set the cell ownership for both interiors to the same faction (as each other and the door), the door will be unlocked in game. When I remove faction ownership from the doo, it will lock. I can't begin to explain it, I can't even reproduce it consistent across different cells. :shrug:
In another cell, there is a door that connects to another interior cell and a door inside the cell. Changing ownership setting on door A (door that teleport to another cell) seems to change the ownership setting on door B (just a door inside the cell), even though I've looked them over to make sure I haven't somehow screwed up something (door A is teleporting to another cell just fine, and the door in the other cell is teleporting to door A, not door B).
I am thinking that perhaps I should stop setting the ownership on doors altogether, and just lock them to let the players know these doors go to off limits areas. But then if I don't set ownership on the door and just lock it, that also means the player can pick the lock in front of an NPC and there would be no repercussions, no?