I am not sure there is any need for special rules for this type of questions, if I understand the type of question you have in mind correctly.
My sister says there is no fraction whose square is $2$ but the calculator on my phone says $1.41421356237$ is the solution which is just $141421356237/100000000000$. Thus I do not believe her but she insist she is right. Who is right my sister or my phone?
I would not see any problem with this question (besides it surely being a duplicate). There is a clear question that can be answered; the story even provides the context.
I would even consider the following as about alright.
My brother says there is no number whose square is $2$ but the calculator on my phone says $1.41421356237$ thus I do not believe him. Who is right my brother or my phone?
That question is somewhat problematic as it is more unclear what the brother meant (or said exactly) when number is invoked. But I still feel one can answer this, explaining that there is no fraction but etc.
Now, if we were to get:
My uncle said square roots do not exist. But I do not believe him. Am I right?
Then, we start to get into unclear territory as there are several things the uncle might have meant or even said (and been correct) or might have misunderstood. But it may still be feasible to answer this, though personally I rather would not attempt it. Yet one might ask the questioner for their background and then give them some response on roots.
Of course, there will also be questions of this form that are too unclear or otherwise unsuitable. Yet, as a rule I do not see any particular problem with this type of question. Indeed, on the contrary, such a questioner usually will be at least invested in their question.
To put this differently, while we sometimes may not know and have reasonable doubts as to what the quoted source actually said, it is not always crucial for us to know this to give an answer. Only we should strive to be clear and precise as to what we answer and use some common sense to correct for likely imprecisions, yet again being precise regarding what one does:
The [literal statement] is wrong [because] but [whoever] may actual have said/meant [something very similar], which is true.