From a simple standpoint of energy conservation, it's obvious the observed brightness cannot be infinite; the article questions the brightness value of the sky,

From a simple standpoint of energy conservation, it's obvious the observed brightness cannot be infinite; the article questions the brightness value of the sky, not whether it is finite. From conservation of energy, for a homogeneous universe, a region around a star must receive as much energy as it gives out. So the total observed brightness of the sky would sum to the brightness of your own star, approximately (but distributed over a solid angle 4pi).