From what I have read your hair doesn’t really wash itself, it’s just that the oils in your hair reach a kind of equilibrium, which doesn’t happen normally when we wash our hair. This is because shampoo is a detergent which breaks down the oil in hair, this then triggers the hair follicle to produce more oil to compensate, however it produces too much which then makes hair greasy. If hair is left for 6-12 weeks these oils become balanced (probably because of a feedback mechanism in the hair follicle) making hair slightly oily, but not as greasy as it would be if you washed it and left it for a few days.
I had a friend who tried this….at first their hair was horribly greasy but after a few weeks it actually looked quite clean and glossy! I think they only lasted about 4 weeks before they washed their hair.