The spin transfer ΔS = 1 response function of 48Ca and 54Fe has been determined by measuring the spin-flip probability Snn for 300 MeV proton inelastic scattering at the Los Alamos Meson Physics Facility, Los Alamos, NM, and TRIUMF. Data have been recorded between 3° and 15° for excitation energies up to about 40 MeV. Except at the largest angles, Snn in the 35–40 MeV range is more than 50% above the isospin-averaged values from free NN scattering, and 25 to 50% above a calculation using Glauber theory and a slab-response function. This enhancement observed with the supposed weakly spin-dependent (p,p′) probe should be contrasted with the apparent quenching observed with the strongly spin-dependent (p,n) probe. There, at 0° and 40 MeV, Snn is only slightly above the (p,p′) values and well below the free values.