I think that Neo touched the source by being granted what we know as super-user or root permissions on the matrix system. This happened when Neo left the matrix when he visited the architect.
How Neo left the matrix in a consolidated summery:
When Neo used the key the keymaker gave him, he exited the program of the matrix, but not the machine's computer network. Think of it like the internet and a unix server:
root at console access --> root at network access --> shell access with root permissions --> network user interface with extended permissions --> network user interface
The people inside the matrix are at user level. Any reprogramming of the matrix does not affect them because the program is running on a buffer allowing for real time reprogramming.
Neo gained extended permissions to control the behavior of the matrix in M1 when he realized that the machines could not kill him inside the matrix unless he believed they could. He can move as fast as they do because his mind is limited only by how fast his neurons fire, not by the limitations of physics.
By unlocking the door to visit the architect Neo, in effect, exited the matrix program in his user session. That would be like telnetting to port 71 on a webserver, crashing it causing it to reboot giving you full root permissions. You can manipulate at the root level but you are not at the root level.
This is as far as we've reached in the first two movies. Neo opted to return to the matrix, instead of trying to gain full root access. Perhaps he feels there is a better way to gain root? Or maybe he is going to attempt to gain console access??