> we want there to be a threshold, because we don't want people (or AI) to ignore obvious emergencies

There's an SF short I can't find right now which begins with somebody failing to return their copy of "Kidnapped" by Robert Louis Stevenson, this gets handed over to some authority which could presumably fine you for overdue books and somehow a machine ends up concluding they've kidnapped someone named "Robert Louis Stevenson" who, it discovers, is in fact dead, therefore it's no longer kidnap it's a murder, and that's a capital offence.

The library member is executed before humans get around to solving the problem, and ironically that's probably the most unrealistic part of the story because the US is famously awful at speedy anything when it comes to justice, ten years rotting in solitary confinement for a non-existent crime is very believable today whereas "Executed in a month" sounds like a fantasy of efficiency.