Matterwave: The reason NC interactions to not appear in the MSW Hamiltonian is that they are equal (up to loop effects of ##\mathcal O(10^{-5})## times the CC contribution). The NC part of the MSW Hamiltonian is therefore essentially proportional to the unit matrix and only contributes to the neutrino flavor evolution with an overall phase. It is therefore customary to drop this contribution and only work with the CC contribution. This is no longer true when dealing with sterile neutrino flavors where the NC part is proportional to the projection operator onto the active states.
Edit: Relatively recent open accessreview on matter effects in neutrino oscillations:
http://dx.doi.org/10.1155/2013/972485
The relevant discussion is on pages 2 and 3.
Carter: Your post goes against the last 52 years of research in neutrino physics (the muon neutrino was discovered in 1962). It is possible you have seen analogies of neutrino oscillations to spin precession (the mathematics is the same), but these are simply analogies. Neutrino oscillations are fundamentally based upon and our currently only confirmation of different neutrinos having different masses.