Philly cheesesteaks aren't really fatty,I don't know if it's trimmed off or what the story is. As for the bread I always heard it was a combo of water and altitude.
Some say the submarine sandwich got it's name in Atlantic city because the bread was baked below sea level.
I say it has to be the water. Lots of places in the philly area that make homemade mozzarella import water from different areas of Philly and New York so maybe the same goes for bread. Kinda like bagels from NYC, same thing.