Everything is inter-related and they influence each other. The question here is what is health?
For example, when I get myself too fit, as in, too strong, then I also become more aggressive and reckless than I feel to be useful for me. It's true, I've tried that. In fact, my most intellectually efficient times, I've been maintaining extremely unhealthy body by all usual standards. Then, which is which.
I'm certainly not convinced that maintaining the types of body that TV/media/fashion/art promotes, is necessarily the best for your brain. At least, this issue deserves serious consideration.