Inside the Matrix designed by the Architect, Neo has the ability to bend and break rules (including ones pertaining to death).
Does Neo have the same ability within the Construct program, which is a simulation of the Matrix written by the Zionists?
I recognize that in the first sparring program, Neo is able to convince himself that he can move faster than Morpheus. This could just be a mind over matter thing, and less of a innate ability in Neo. Who is say that others couldn't also beat Morpheus in the sparring program?