Is a Lambertian reflector illuminated by a smaller fraction of the incident radiation when it's tilted?
I see some problems in the quote you posted.


  In effect, a point rotated around its normal vector will not change
  the way it reflects light.


This is true, because a Lambertian reflector will never change the way it reflects light. The underlying principle stays the same. Also, Lambertian surfaces are isotropic, so the amount of reflected light won't change either (which is probably what this sentence is aiming for).


  However, the point will change the way it reflects light if it is tilted away from its initial normal vector since the area is illuminated by a smaller fraction of the incident radiation.


Again not true, because the principle doesn't change. The amount may change, except for the special case that the cosine is &lt;= 0 before and after the tilting. The amount does not necessarily grow, except if we define that the cosine equals 1 before, i.e. that the normal points directly towards the light source.

This whole paragraph should probably be rewritten to be less ambiguous. Including isotropy could make it more complete.