It's even worse than that. I am using theology more as empirical example of what you get when the specific features are part of thought process. Ultimately what matters is the features in question. If the features were 'wearing same type of hat', then that wouldn't mean a lot, if the feature is lack of attempt to reason in the least sloppy manner (for example the computational complexity things reasoned about using math), then that's the shared cause, not just pattern matching.

Ultimately, what an intelligence would do under rule that you can just postulate it smart enough to do anything, is entirely irrelevant to anything. I do see implicit disagreement with that, in doing this sort of thinking.