How would they know she is the "working" captain? She could be dead heading on the jump seat for all they know. Crews are dead heading all the time in the USA.
As a retired major US passenger airline Captain, I know a couple of things about USA airline procedures.... The agent knows if there's a jumpseat rider. The agent has to assign all seats (including the jumpseats) in the computer, for weight and balance if nothing else. Even presuming that the FO pulled up the paperwork, the agent(s) know who is working the flight. Regardless of whether the captain showed up and boarded with the rest of the crew, or boarded late, the agent knows who's going down the jetbridge and where they're sitting... including the Captain's chair.