Since they're a stranger, what's taboo about it? I can't imagine anyone being doxxed by the additional information requested...

They didn't demand, they asked. If you seek to represent your position on internet forums then you're going to need to tell people your position.

As access to specific resources is a central part of the complaint it seems perfectly reasonable to request more details. They can be general, like "I can't book a psychiatrist" or "I need specific drugs that are in limited supply".