Does gravitational redshift support the curved-spacetime interpretation of general relativity?

It has been overlooked that the wavelength of a photon in the gravitational redshift experiment cannot change along with its frequency due to the law of conservation of the photon momentum. As both frequency and velocity change in this experiment the measurement of a change in a photon frequency is in fact an indirect measurement of a change in the photon local velocity. This means that the local velocity of a photon depends upon its pre-history (whether it has been emitted at the observation point or at a point of different gravitational potential) a result that contradicts the standard curved-spacetime interpretation of general relativity according to which the local velocity of light is always c. This result, however, does not contradict general relativity itself. PACS: 04.20.Cv, 04.20.-q