All things are possible though the love of Apollo
It has been my experience that a United employee with computer terminal, the right motivation, and perhaps the willingness to violate policy (or ignorance of policy), can do pretty much whatever they want.
For several years (and completely undeservedly) I was lucky enough to be in what amounted to United's "VIP" program, which consisted of small offices in the concourse at ORD, JFK and SFO, staffed by helpful concierge types - I believe this was the precursor to Global Services (my experience there ended with a job change about 12 years ago). In my case, it was a guy named Frank at SFO. Wherever I was in the UAL system, if I was having some kind of difficulty, I could call Frank, and with a few keystrokes the matter would be resolved. Upgrades for waitlisted cabins magically cleared, often because the booking code changed from (e.g.) NF to F. Oversell the flight (a little more) to get me on it? No problem. Routing or other change that violates the fare rules? Wink, wink, nudge, nudge. Rushing to make your connection? I'll just phone the zone controller and ask them to hold the gate a few minutes (can you imagine that sort of thing now, with "on-time zero"? lol).
This unique (for me, anyway) relationship provided an interesting window. My assumption, having worked with large, complex computer systems in the past, was that United's system had different levels of privilege, and Frank was permitted to do things that other agents were not. However, the more I talked with Frank, and, later, as I tried to weasel my way into Frank-like accommodations in a (chillingly) post-Frank world, the more I became convinced that this isn't the case.
Bottom line: I know there are audit trails in the system, and agents are often held accountable for their changes. But I also believe that there are very few structural controls in the system that actually prevent agents from doing exceptional things, or that the controls are easily (and often accidentally) overridden by even frontline/unprivileged users.
I don't believe agents "lie" in the malicious or deceitful sense. But I do agree that, often, when they say they "can't" do something, what they mean is they are "not permitted by policy" to do it, rather than that it is technically impossible or prevented by the system.
Maybe this is consistent with your experience when calling for changes, as well? Isn't it strange that the burden is on the agent to read the fare rules in order to figure out how much to charge you for the change, or whether it's permitted? Wouldn't you expect the system to do that, by responding to the agent's request with "illegal change" or "collect $150" or something?
It's nice when it's an error in our favor, as the OP experienced - but the flip side of this effect is the well-known difficulty United has in establishing a consistent customer experience. How many of us carry around copies of various rules in order to "prove" to an improperly trained agent that we are entitled to this or that change? And we all know the golden rule of UA reservations: if at first you don't succeed: try, try again. This is a direct result of inconsistently applied policies, an (IMO) inescapable effect when they're applied by humans rather than the 'puter.
I realize that automating this kind of policy or rules enforcement is no simple task, especially for a system so complex. But it's certainly not impossible, and I suspect it would yield tangible benefits in terms of customer experience and perhaps recaptured revenue.
Any thoughts on why United hasn't put these structural controls in place? Too much investment required? Fear that they would wind up causing more harm than good (by constraining goodwill gestures, etc.)? Constrained by the legacy nature of the systems themselves?