Once a human has the class of Fighter (or Rogue), they are capable of doing supernatural things, but that doesn't make them supernatural, they are still simply human.
This is accomplished through class features, subclass selection, and feat (if used).
This is why making a blanket statement "Humans are supernatural" doesn't fly. You might not particularly care about those nameless masses, but they are out there. Now, Human PCs and creatures/NPCs can do supernatural things, but that doesn't make them supernatural in-and-of-themselves.
Of course it's allowed, but those house-sized pumpkins aren't due to Joe Farmer being "supernatural". Some visiting fey helped, or the seeds were magical themselves, or the water was blessed, or whatever. I'm sure Joe Farmer is a very skilled and accomplished farmer, but not supernatural.
A dwarf with magic and a dwarf without magic could be due to the aforementioned reasons. It could be class or likely a feat. Even a dwarven fighter can easily gain magic due to the EK subclass, it doesn't have to be a "wizard class" or something.
You realize you are basically making my point? Sure a human fighter can do amazing things, but it doesn't make them supernatural or magical because they are human, does it?
Right, but it is the training (class, NPC or creature stats) that can make a human soldier a super soldier, not because they are human.