I completely agree with Luke on this point and can provide proof that this is the truth in the movie that most people ignored.
The "real world" was not the real world, but simply another layer of Matrix that allowed the people who were not happy with the original Matrix to escape and believe they were free without actually posing a real threat to the machines. The war they were fighting against the machines was a virtual one and none of them had actually ever left a pod. They were all still connected to the Matrix.
The reason that Neo could control the machines is that the "real world" was just another simulated layer. This is also the reason that Smith could transfer into a human. The way the movie confirmed this truth is that when Neo lost his vision he could see the Matrix, but this time the code was yellow instead of green. The "real world" was simply another Matrix, but this different reality was yellow code instead of green.
If Neo was truly in reality he would not have any magical ability to control the machines. Smith would not be able transfer his consciousness into a real person. The real world is not based on computer code so Neo would not see the world as such if he were truly in reality. The "real world", the Matrix with the yellow code was created so that disenfranchised people could escape the green Matrix and yet not be a real threat to the machines as the war they were waging was a virtual one and had no effect on the real machines in the true reality. It also kept them enslaved even though they thought they were free.