This is a lot easier than what you guys have articulated. Think of Neo as a machine's version of A.I.
Neo is a pod human. All pod humans are created by the machines. Since he's the one, the way he was created by the machines allows him to do things (i.e. fly and stopping bullets) in the Matrix that no other human can do.
The only way he can do the ^ isn't because his RSI in the Matrix grants him "master user status," it's because his physical body was uniquely created when the machines made him. Therefore, the reason he can do things in the Matrix that others can't is because the machines made his physical body differently from those of other humans and that physical distinction allows him to also do things outside of the Matrix (i.e., in the real world) that others can't do (i.e., the ability to see the energy machines have and stop them, presumably through wireless powers).
Think of Neo as a machine's version of A.I.:
Lastly, to analogize it, think of Neo as a machine with A.I., the machines are humans, and the pod humans are thoughtless machines (like a dish-washing machine or a lamp).
The machines use humans to help them live (similar to why humans, generally, created machines) and the machines created A.I. (in this case, Neo) as another means to survive (in this case, to make sure the Matrix is fail-proof). Though humans created A.I. to allow them to survive, but screwed them over in the end, the same happened when the machines created Neo. Just like A.I. f@@@ed humans over, Neo f@@@ed the machines over because he's not like every pod human they created; he's got self-control, just like A.I. Hence Neo used his "outside the Matrix" powers, which were granted to him by the machines, against his creators, just like the A.I. machines used their powers (in this case, intelligence), which were granted to them by humans, to rebel against their human creators.