I go by a personal theory of 'functional equivalence'. It doesn't matter what intuition is 'made of', as long as the language I use to describe it is consistent. So it feels supernatural to me, and seeing it that way helps me be more aware of my intuition, which is a good thing. If you peeled away the layers, you'd find at the base that I believe there is some 'natural' mechanism by which the 'supernatural' occurs. But, as with martial arts, explaining at that level of detail, we'd never 'get it'. You'd be one of the blind men arguing about the elephant. You'd have a hard time being able to *act* on the (quite useful) intuition, nor could you break bricks with your bare hands.
The whole body is the brain; there are neurotransmitters drifting through all parts of the body, and doing who knows what extra functions. Some of our bodily organs produce neurotransmitters in response to certain conditions. Particularly the gut. Believe me, your intestines are doing some serious 'thinking' all day long, and the 'gut feeling' you get, that's a component of intuition.
Um, sorry if I'm agreeing with you at excessive length. I like to hear myself think. :)