I've not flown United, but I've had very similar experiences with many airlines when using TWOV, especially when flying from "unusual" airports that probably don't get many people using TWOV. You have to stand your ground, insist on a supervisor if necessary, and sometimes coach them through using timatic. I've not been denied boarding yet, but I imagine it will happen one day, and that's a risk when using TWOV.
Edited to add: this kind of thing is actually a risk any time you do something a bit outside of the "norm" when traveling. I'm sure many of us have encountered situations where a person in a position of authority, such as a check-in agent, knows a lot less about something than we do, but isn't willing to admit that, and as a result you have this kind of impasse.