You're totally right on that first point. We do love our absolutes.
But I'd have to disagree with your second point, slightly. In fact, I'd say generally audiences are much better at just taking these things at face value and excepting them, whereas fanboys parse out every single element until the emperor is naked, often to deliberately reaffirm the point they've made in their heads. From my experience, Batman is pretty well known for being, if not a SUPER GENIUS, at least the superhero most likely to be a "crime solver" rather than a "crime fighter."
You're right when you say he doesn't do ENOUGH detective work for Batman, but it's still enough to set him apart from most superheroes, like Spider-Man or Superman, as "the superhero who is also a detective."
Get what I'm saying? I think the awareness is there. You see it in media. "Batman's a scientist!" Homer goes. I don't think audiences distinguish enough to say "Batman's not enough of a scientist in this one!" They still think of him as a scientist, even if he's not playing with test tubes on screen in this particular movie.