Does it help if I add the qualifier "hypothetical" or "possible"?
I.e., All possible pro-snake-handling gods are gods, but not all possible gods are pro-snake-handling gods.
Otherwise I'm not sure I follow what you're saying...
Does it help if I add the qualifier "hypothetical" or "possible"?
Yes. (And I only mentioned the exception because it surprised me that the near tautology had a counterexample.)
Here's the new thread for posting quotes, with the usual rules: