Phonon polariton (PhP) nanoresonators can dramatically enhance the coupling of molecular vibrations and infrared light, enabling ultrasensitive spectroscopies and strong coupling with minute amounts of matter. So far, this coupling and the resulting localized hybrid polariton modes have been studied only by far-field spectroscopy, preventing access to modal near-field patterns and dark modes, which could further our fundamental understanding of nanoscale vibrational strong coupling (VSC). Here we use infrared near-field spectroscopy to study the coupling between the localized modes of PhP nanoresonators made of h-BN and molecular vibrations. For a most direct probing of the resonator-molecule coupling, we avoid the direct near-field interaction between tip and molecules by probing the molecule-free part of partially molecule-covered nanoresonators, which we refer to as remote near-field probing. We obtain spatially and spectrally resolved maps of the hybrid polariton modes, as well as the corresponding coupling strengths, demonstrating VSC on a single PhP nanoresonator level. Our work paves the way for near-field spectroscopy of VSC phenomena not accessible by conventional techniques.