No, you can't. If somebody treats you with suspicion, it's because of a combination of their news intake, their culture, local events, what their friends and family would think, the way you present yourself, and many other factors. You can always ask somebody to state their reason as a simple "if-then" statement, and they can make one up on the spot, but it'll be so oversimplified that it's basically a lie.
> So maybe we don't necessarily need fully interpretable models but simply a way to ask black-box models specific questions about their state, e.g., "To what degree does a person's age influence the output?".
You can already do that. Just change that number in the input and see how the output changes. To that extent, even the most black box AI model is more transparent than human decision making.