It has been suggested that variations in the solar neutrino rate measured by the 37 Cl experiment that appear to be anti-correlated with the solar cycle phenomena could be explained in terms of an MSW mechanism by solar matter displacement. These matter displacements might be brought about by magnetic fields in the sun's convection zone. However, such inside displacements result in solar surface displacements. The observed limits of solar radius variations constrain the inside changes. Using these constraints together with calculations based on the MSW mechanism, we show that the corresponding neutrino rate variations are very much too small to explain any experimental observations.