The biggest controversy seems to be over where private buses that don't have their own private loading/unloading infrastructure can stop and load/unload. Some cities tolerate unofficial use of public bus stops, or look the other way when buses load/unload in a blatantly illegal way (by just stopping in a lane of traffic and blocking it, as "Chinatown buses" typically do). Other cities are less tolerant of that. But when private buses actually pay for their own private loading/unloading facilities on land they either own or properly rent, like Greyhound does, then there's no problem.
Cities don't allow private busses to obtain curb rights in the first place.
Greyhound is intercity, not intracity. Useless for this purpose.
The only controversy stems from taxis & muni busses protecting their turf.
You may know them as Jitneys: http://en.wikipedia.org/wiki/Share_taxi