"How would you handle it if X came to you and said Y..."
Or, if they already have past management experience, ask for an example of a time when something like this happened, and how they handled it, and what they learned. Or maybe start with this and then propose a hypothetical as a backup if the candidate doesn't have anything off the top of their head?
I don't know, just doesn't seem necessary to jump up to that level of negative self-generalization with the candidate just to "test a management skill." I mean, come on, "people who don't think very highly of you"??? Who is "people"? Why are you generalizing like that?
"Hey, so, everything bad that's ever happened to you at work, so, like, what did you learn from that??"
I didn't get either one of those jobs, now that I think of it.
I would instead present them a situation which tests the same skill, that way it's clear I'm testing them.