The matrix made him only think he was a programmer.

Why do you say that? Just because the humans plugged into the Matrix are given false stimuli does not mean that they are unable to perform actions of their own volition, even write code, just that the events pertaining to and consequences resulting from the actions would be represented in a virtual environment. The very fact people can be retrieved from the Matrix and go on to adapt in short order to the real world IMO indicates that their experience as brains in vats includes intentional actions. Is it really believable that the human brain grown entirely in a position of passivity could be retrained in adulthood to carry out actions?

I've always interpreted the Matrix as a form of symbiosis in which the machines rely upon humans for energy (silly really, why not use cows?), and humans are permitted to live virtual lives indistinguishable from the real thing in enchange. It's quite conceivable to me that the individuals inside are by and large free to build a world from their own desires and ambitions. Neo may well be a real programmer, using a language every bit as real as Perl, with the caveat that if Decartes is correct and it's possible that an evil genius could convince someone that 2 + 2 !=4 then by extension, for example, Turing completeness could mean something different in the Matrix. But more than a few people disagree with Descartes on that point :)

Update: Ooh, fuel for the fire: Trinity hacks! :^)