Please help with the rules of the Hardest Logic Puzzle!

I'm working on that Hardest Logic Puzzle Ever, the one with the three gods, and I keep running into a big question mark. NOTE: I don't want the answer to the puzzle! I'm just asking a question about the rules! Thanks.

The thing is, I keep getting outcomes where a god's head explodes. For example, suppose you ask one of the gods, ''If I were to ask the other two gods whether your (the god I'm talking to) name is Random, would exactly one of them answer yes?'' If you're talking to True, True knows that False would say yes, but they don't know what Random would say, so True couldn't answer the question, hence their head would explode. Asked the same question, False would explode for the same lack of information that would enable them to lie properly. If, however, the question received an answer - any answer other than a head explosion - you'd know you were talking to Random.

This explosion effect applies to many possible lines of questioning, yet the rules don't mention anything about the other gods being able to predict what Random will say. In fact, the rules sort of seem to indicate that Random's answers can't be known ahead of time. So, QUESTION - which is NOT A REQUEST FOR THE SOLUTION TO THE PROBLEM, ONLY A QUESTION ABOUT THE RULES: Does anyone know of a rule about True and False having an ability to predict what Random will say? Because, much though I like the idea of solving the problem by blowing up heads, I don't think the puzzle's designer intended that as the answer.