We demonstrate that the emission characteristics of site-controlled InGaAs/GaAs single quantum dots embedded in photonic crystal slab cavities correspond to single confined excitons coupled to cavity modes, unlike previous reports of similar systems based on self-assembled quantum dots. By using polarization-resolved photoluminescence spectroscopy at different temperatures and a theoretical model, we show that the exciton-cavity interaction range is limited to the phonon sidebands. Photon-correlation and pump-power dependence experiments under nonresonant excitation conditions further establish that the cavity is fed only by a single exciton.