I'm guessing you mean flying out of MEX to a destination inside Mexico? If so, then the agent was correct. Under OneWorld lounge access rules, you must be traveling on a OW-marketed, OW-operated flight in order to get lounge access. BUT, currently there are no OW-marketed, OW-operated flights operating wholly inside Mexico. (This soon will change once MX joins OW.)

Of course, if you are a paid Admirals Club member, then it doesn't matter what airline you're flying, or even IF you are flying at all. HOWEVER, another, unrelated issue is terminal access. The Admirals Club is located in the terminal from which AA operates--the international portion of the old terminal. If your flight departs from the new terminal, or the domestic portion of the old terminal, then you wouldn't be able to get through security, and thus you can't access the club even if you are a paid member.

YES, under current rules:
AAdvantage Executive Platinum® members may use the Mexicana Lounge on the day of travel when traveling via Mexico City on an American Airlines, Mexicana or a codeshare flight operated by either carrier regardless of the class of service flown, EXCEPT Mexico City (MEX).

This policy seems to be an interim, temporary solution until MX joins OW and the normal OW lounge access policies come into effect. (But let me just say that the part I quoted above seems incredibly unclear. "Traveling via Mexico City" but also "EXCEPT Mexico City?")