It takes a few seconds for the desk they call to re-sync the ticket. I know this because I've had it done at least 100 times in the past. I think you may have jumped to the wrong conclusion - nothing to do with any computer system.
More likely the agent made the change incorrectly, or they can't get in touch with the person who can make the change in a few seconds.
Now I totally agree that they shouldn't have to call anyone, but it doesn't take 30 minutes to make the change.