I have to say - Tinch's argument is the one I've seen here which differs from my own, but shows a lot of originality in its analysis and I think it's interesting.
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).
While I could see this being justified in-part due to canon, where the Architect explains that the "one" is a systemic-anomaly that basically embodies all the leftover subconscious rebellion from the Human psyche, and a depository for incompatible algorithms. Which must be re-inserted into the Matrix so that people will be able to "choose," once again, if even on an unconscious level (as he explained about the Oracle, or "Jesus'" idea). The answer was simple to me even from the first time I saw the conclusion to the Trilogy. Remember, Agent Smith was able to supersede the matrix by taking that phone call - thus using the digital-translation mechanism of the telephone, in order to get into that other character's mind - becoming his consciousness. This brought Agent Smith out of the Matrix, since while inside the matrix a consciousness is virtual, anyway (whether you're Human OR machine). So why couldn't it work the other way around? It's not coincidental that at roughly this same time in the second installment, Neo has grown so accustomed to the "sense" of how the Matrix operates (after-all, being able to see in code and everything), that in a way dualistic to how Smith escaped, he is actually able to use Matrix-like powers against them from OUTSIDE the virtual-construct.
Keep in mind, the Matrix was constructed by these very machines - so it's not surprising that while Smith has the ability to transcend the "virtual world" into the real, but the flip-side of that is Neo being able to transcend the "real" world's limitations directly through his accumulated interface with the nature of these same machines. Remember, when he entered Smith's avatar in the dramatic conclusion of the 1st movie? Well, I believe that's a CLUE to what the Architect would ultimately confirm in the second movie, and that is Neo is somehow integral to the survival of the Matrix. So there's no reason to object to the possibility that this fundamental connection couldn't supersede that virtual form - after-all, the minds behind the Matrix have a physical basis OUTSIDE of it as much as the actors jacking into the Matrix do as well. It's the opposite of bleeding in your chair when you get punched too many times while connected to the program, basically.
It's no coincidence, therefore, that Smith in Bane's body ends up lying in the medical-bay directly (and oppositely-positioned) from Neo, after this manifestation of his intrinsic connection to the Machines outside in reality actually drains him of all his energy - hey, I'd be exhausted too after something like that.