HDRI is a type of reflection map that goes onto a model. True HDRI can project light. Fake HDRI simply is a reflection in an object. Global lighting is a fake form of radiosity, which is different from HDRI. The bryce forum is well advanced in faking HDRI and radiosity in software that does not have these features. So here's a P5 render with fake HDRI. I just plugged an image into the reflection and diffuse nodes on a primitive sphere with a copper texture to it.