On occasion, I like to think that words have intelligible content. If you aren't comfortable with that, and in the context of a game that reduces qualities to numbers and discrete categories no less, then I don't see much productive coming of it. Role-playing, necessarily involves reducing characters to concepts and characteristics that can be conveyed to other people you're playing with. If you can't do that, the game is never going to be able to get off the ground, nor can you have a meaningful discussion about characters. Your only response to that, in the context of RPGs and to some extent character analysis/literary criticism, is not so veiled insults.
The idea that there is some sort of logical impossibility that a character can be a hero and not be intelligent in its conventional, plain English, ordinary meaning, is absurd. Hercules alone, an important mythological hero for millenia, should be a sufficient counterexample. Likewise, Beowulf, Fafhrd, Kalam Mekhar, and Spike Speigel have never been renowned for their intellect. Comic book characters are a little hard to peg down due to various incarnations, but, off the top of my head: Human Torch, Gambit, Namor, and Hawkeye have never been great thinkers. I don't know if I'd call them idiots, but intelligence wouldn't be cited among their strengths. Hell, neither Luke Skywalker or Han Solo seem particularly bright, as noted by a certain princess.
Unless by "smart" one means "capable." That wasn't the context of the original post that started this tangent, which specifically calls out mental abilities and wits. It's also not what the word generally means. And, it also doesn't actually get to the heart of anything interesting except for the very uncontroversial point that heroes probably need to be good at something.