The scattering of light at a metallic nanoparticle in the vicinity of a SiC surface shows a strong peak around the surface phonon polariton resonance of the SiC substrate in the midinfrared spectral region. Close to the surface, the polarized particle couples to localized phonon polaritons. This near-field interaction shifts the peak to lower frequencies and causes a splitting into two modes for distances below 5 nm. We analyze this phenomenon by applying an accurate numerical three-dimensional model based on the multiple-multipole method. The results are compared with the predictions of the analytical dipole model as frequently used to explain the contrast in apertureless scattering-type scanning near-field optical microscopy. We find a qualitative agreement but the dipole model turns out to underestimate the spectral shift quantitatively.