The agent was wrong.
The policy stated on BA's site is very clear about it:
Lounge access is available to Emerald and Sapphire level Members of any oneworld airline frequent flyer programme.
Additionally, the
Oneworld policy has similar wording and lists all exceptions - CX emeralds on domestic US itineraries are not listed as exceptions.
What she said would be correct if the lounge she was responsible for was an AA Admirals's Club and you were an AA EXP on a domestic itinerary.