If authority just counts as evidence

I have an intuition that insofar as a person is fallible, what she says can only be authoritative over what I believe when what she says counts as strong or overriding evidence. Maybe what she says has sway over what I ought to do regardless (even in the case of a mistake) but she cannot influence what I ought to think unless she's an epistemic expert.

Here's a scenario that sheds some light on why my intuition might be off:

I'm on the roof of a burning building and need to get to the building across the alley. The only way to cross is by walking a narrow plank. Firefighter Jim says to me, "Go ahead, it's safe to cross." If there is a net below that I don't know about (because I refuse to look down or something), then it seems obvious that Jim is right, regardless of my skill in balancing. If there is no net, the probability that Jim is right decreases significantly. Is he an authority in both cases? The issue arises in the second case: the reason I have to cross is explained by the circumstances- the fire quickly rising in the building, threatening my life if I stay put. I don't need Jim's authority to explain why I ought to cross. But ought I to believe it's safe to cross? All the stories I can think of would just explain why what Jim says is authoritative only for pragmatic reasons. If I believe him and the statement is false, I still may have a higher chance of making it over because I walk across more confidently. But maybe Jim knows this; then it looks like there's a real reason I ought to believe him and do what he says, not just do what he says.