It shouldn't, under the assumptions they are opening up with. Inverse square law twice is appropriate for an approximation that the reflection is entirely diffuse because you assume that the diffuse reflection is uniform in all directions away from the illuminated surface. A single inverse square law is appropriate (with both distances added to each other before squaring) under the approximation that the reflection is specular.
I’m guessing it’s because the detector is then working with power, not amplitude. The whole 10 log vs 20 log thing with dB.