Fake name + refuse Liza = dead end?

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Fake name + refuse Liza = dead end?

So I've just lost two characters to Sakinaw, both times I arrived in blue sash, didn't tell my real name, talked to Liza and refused her offer (twice), [hiding] her body afterwards. As far as I can tell that puts the player in a no-win state, leaving only getting killed at the exit or getting killed upstairs. Shouldn't the player be able to talk to the king anyway at this point? Maybe with a different set of skills it plays out more organically, but for me that [hide] was the only point at which I could use a skill, and it's entirely pointless in the end.
Or am I missing something and there's a way to unlock that door to the north? I had lockpicking/hacking/trapping/medic/hiding and there were no other prompts.

I try to avoid spoilers as much as I can, but while searching I skimmed the wiki article. I know I could probably solve the encounter differently / easier. But I'm interested to know whether this particular dead end is intended or not, and nobody on the Internet seems to have refused her offer or something.