“Alaska Airlines Mileage Plan MVP Gold and MVP Gold 75K members are not eligible for access to oneworld member airline lounges when travelling solely on North American flights within or between the U.S., Canada, Mexico (except Mexico City), the Bahamas, Bermuda and the Caribbean.”
“American Airlines AAdvantage members, regardless of their tier status or class of travel, are not eligible for lounge access when travelling solely on domestic U.S. flights”
I don’t believe you should have been admitted.