Should we understand this to mean that people are only allowed to ask about questions that they personally face?
No, I wouldn't frame it that way.
Are these questions intrinsically hypothetical (and therefore off-topic), since the person who's actually posting the question doesn't have the problem?
I don't think they are hypothetical. They are 100% real, as it's something that is happening to someone (not the OP perhaps, but still real).
Or are there some circumstances under which they're acceptable?
I think that such questions should be taken as any other question, and its quality and clarity expected should be good, as with any other question.
Sometimes OP may not be willing to say they are the ones that are experiencing this, and thus say that "this happened to a friend". If indeed this is happening to a friend, and the post lacks clarity or details, then one should request clarification and improvements as one would do with any other question.
For example, I once asked a question that didn't happen to me (happened to my SO at that time, who also doesn't have a SE account). However, I wrote the post with all details and clarity needed to obtain help. Such question was very well received (100+ votes) and got very helpful answers.
In the end, it didn't matter it wasn't myself the one going through that. The question was good, was realistic, and judging by the 100+ votes and several great answers, I am sure it helped other people navigate through the workplace.