It doesn't have anything to do with intellect.

And complexity ≠ intellectuality

I mean, I know very little about music theory.

But I bet if I picked up a couple books on it and spent a month reading them, I could give a basic breakdown of just about every pop song or anything in the electronic music genre. And I listen to a lot of music. From pop to punk to hardcore to pop punk to post hardcore to new wave to synthpop to EDM to EBM, etc.

I'm not saying it's easy to create good music in any of those genres, it's absolutely not.

When it comes down to theory and analysis though, the complexity of "classical music" absolutely does need much more of an intellectual understanding than any of the genres I mentioned.