Within an isospin-and momentum-dependent transport model for nuclear reactions at intermediate energies, we investigate the interplay of the nucleon-nucleon short-range correlations (SRC) and nuclear symmetry energy Esym(ρ) on hard photon spectra in collisions of several Ca isotopes on 112 Sn and 124 Sn targets at a beam energy of 45 MeV/nucleon. It is found that over the whole spectra of hard photons studied, effects of the SRC overwhelm those due to the Esym(ρ). The energetic photons come mostly from the high-momentum tails (HMT) of single-nucleon momentum distributions in the target and projectile. Within the neutron-proton dominance model of SRC based on the consideration that the tensor force acts mostly in the isosinglet and spin-triplet nucleon-nucleon interaction channel, there are equal numbers of neutrons and protons, thus a zero isospin-asymmetry in the HMTs. Therefore, experimental measurements of the energetic photons from heavy-ion collisions at Fermi energies have the great potential to help us better understand the nature of SRC without any appreciable influence by the uncertain Esym(ρ). These measurements will be complementary to but also have some advantages over the ongoing and planned experiments using hadronic messengers from reactions induced by high-energy electrons or protons. Since the underlying physics of SRC and Esym(ρ) are closely correlated, a better understanding of the SRC will in turn help constrain the nuclear symmetry energy more precisely in a broad density range.