While it may have taken only a few keystrokes, what we don't know is what else the GA had to do before the flight. Also the aircraft servicing wasn't known until after the door was about to be closed (this has happened to me many times this year).
What is known is that United corporate insists all aircraft are off the blocks on-time and hold the GA responsible for this in terms of the customer service side of things. This has been stated in other threads.
I can say that I have been denied being put on the stand-by list before as well, and usually when it is this close I will ask nicely if there is still time to process stand-by pax.