Earlier quoted context omitted.
Staring directly at a light source strains the eyes more than watching reflected light.
By what mechanism of action? It can't possibly be true in general: e.g. staring at the reflection of the sun in a mirror strains the eyes more than staring at a candle.
Firstly staring directly at a light source means that you are seeing most the rays directly. The only attenuation you will receive will be scattering from the medium - presumably air which will be low.
Seeing it from a second surface adds more effects - the surface may have absorb some of the light. Any real surface is also not going to have perfect reflectivity (everything from scattering, internal diffraction and destructive interference could occur). In short there will be loads of secondary/tertiary effects causing attenuation. Someone also mentioned polarisation, I also wonder about interaction between reflective surfaces which could cause additional attenuation via interference but the physics of waves has never been a strong point.
The other major factor is the physiology of the eye - we evolved from a world that didn't have abundant light sources and it's hard to know the effect of focusing on a source of light that differs from the ambient profile.