Without avalanche effect, without quantum cutting phosphors etc, the quantum efficiency for visible light photons can not exceed 100%: a photon of suitable energy (i.e. higher than the bandgap) would liberate a single electron-hole pair with the excess energy lost as heat. Some electron hole pairs may recombine before completing a loop around the external circuit, lowering the total quantum efficiency.
A SPAD uses the avalanche effect: the applied reverse bias being so strong that the electron of the initial electron-hole pair is accelerated to sufficient energy to knock out and liberate more electron hole pairs, so that you can have quantum efficiencies exceeding 100%: as a function of the applied reverse bias there is an extra mean multiplier constant describing how many electron-hole pairs will be liberated due to a single photon striking.
>This explanation isn't consistent with my understanding.
Its probably because you misremember, the quantum efficiency of SPAD's is higher not lower than that of your average CCD sensor.