The error in Modo's reflective rendering has nothing to do with UV mapping issues as far as I can tell. For the purely reflective images I've posted I have manually set the material to be a single BRDF layer with diffuse=0 specular=0 or 20 (doesn't matter) roughness=0 reflection=100 and blurry reflections off, so UV mapping shouldn't come into it.

I think Steve just didn't zoom into the appropriate part of the render, and also has a "busy" background which obscures the issues as well.