I don't think so. I think it's because the texture is already photo-like, and then there is a normal map applied on top of that. It basically creates two layers of shading that don't fit together. Few games manage to avoid that problem.
Interesting hypothesis. I think this would predict that you’d get more realistic results if you were using “bare, unlit” textures (e.g. texture images + normal maps created by using 3D scanning or even computational tomography, as you would if you wanted to 3D-print a copy of the object) and then applying regular normal maps to them. Anyone have screenshots of 3D game objects that were explicitly mentioned as being authored this way?