It's possible that it just appears that the normals are okay, but some viewport modes show them as reversed, which is how they are.
The lighting and viewport modes should not affect any normals. But some faces may show up looking fine, especially if 2-sided lighting is on. To see how the normals actually are, select your object and go Display > polygons > Face normals, and green lines will show you which way the normals actually are. Hope that helps.