I wouldn't be too concerned about what the computer thinks is going to happen. I don't actually understand what you mean by the "computer is programmed", maybe you mean that the posted departure time will shift two hours when a short-call is involved. Maybe you mean that ther's an automatic two-hour window started right when the call is made? Either way, times get adjusted according to the reality on the ground.

There is a clear understanding as to what is "reasonable", and even if there isn't, it can be discussed after the fact. My understanding is that the expectation is for a person to show about two hours at one airport. The other pilot would most likely have prepared everything, which explains why there is no difference between show-time and push-back. Essentially, the expectation is that you will show up, but will not need 1:00 (domestic) or 1:30 (int'l) to push from that point.