The no-disturbance (ND) principle states that, for any three observables A, B, and C such that A and B are compatible, and A and C are compatible, the probabilities of outcomes of A do not depend on whether A was measured with B or with C.
As far as I know, the definition of non-contextuality is similar to the ND principle. People always take above statement as an example to introduce what is non-contextuality. But we all know quantum physics is contextual. It seems that contextuality contradicts the principle of no-disturbance.
So, what is the difference between them ? Why is the ND principle a more fundamental hypothesis ?