I mean in general, not just MC and not just during the course of this game and not just in relation to murder questions. Vast majority of people would not befriend or interact with mystical lie detectors, no matter the competence level. Especially not people with giant secrets who can't afford such risks. And for the few that do, almost certainly out of some obligation, they would at least have some kind of longstanding policy to make the relationship (colleague/friend/sibling/lover) work. No questions, short statements, keep every statement as broad as possible, written replies, etc.
And mind you to put it into perspective, polygraphs are inaccurate as hell and yet virtually no one would willingly attach themselves to one on a regular basis. People value privacy and do not appreciate things that threaten it. Truthsayers would for sure be stigmatized in some way if they have the inherent ability to expose people's deepest vulnerability. If they do put up with them, they certainly wouldn't be kind. And most likely, the stigma would be far more brutal as unlike most persecution they do have a good reason to hate. The only truthsayer in town would probably need protective detail at all times.