That story though ends a little unfortunately, with Superman accidentally shocking Robin with static energy he'd built up without realising, and it ends with Robin realising that Superman ISN'T really human and is a little frightning
Your memory is correct. The story is titled "Fear of God." That phrase appears as Dick thinks it's time he put "the fear of god" into some crooks the way Batman does. But by the end, that phrase also refers to Dick's awe at Superman's godlike powers. I don't think Dick buys into Bruce's suspicion of Superman as an alien, but he's grasped just how much more powerful this friendly visitor is.
Obviously, we readers come to that story with knowledge of the decades-long friendship of Supermen, Batman, and Robin, so it doesn't negate the relationship we expect will develop. But it adds another wrinkle to it.