Recent scanning tunneling hydrogen microscopy (STHM) experiments on PTCDA (perylene-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride)/Au(111) have shown unprecedented intramolecular and intermolecular spatial resolution. The origin of this resolution is studied using an accurate STHM theoretical simulation technique that includes a detailed description of the electronic structure of both the tip and sample. Our results show that H2 molecules are dissociated on the Au tip; the adsorbed H atoms change the density of states at the Fermi level (E(F)) of the tip, increasing its p-orbital character and reducing the s-orbital contribution. Also, due to the interaction with the H-decorated tip, E(F) is shifted to the middle of the PTCDA lowest unoccupied molecular orbital peak, increasing dramatically the density of states of the sample at E(F). These effects give rise to the enhanced STHM resolution.