Doesn't it depend how you define style and class?

If for you having style means conforming to some common reference of what style is, that in itself implies average. Highly intelligent people often act differently from the average. This is interpreted by some as social ineptness or non conformism. And hence as lack of style.

But on the other hand, you could say intelligent people have a greater ability to observe, to understand, and to act in a dignified way. But this is also something that can also come from education and from growing up in the right environment and does not necessarily require an extremely high intelligence.

"having style" is often a way for the middle class to differentiate themselves from the working class. Doing subtle things that the others are not even aware that express who is part of it and who isn't. Only they don't see that the upper class has similar codes that exclude the middle class. Saying somebody has class can thus reflect that you associate with their social class.