She should have scrolled down the page: 'If you've earned Emerald or Sapphire through an airline other than American or Alaska, you are not required to have an international itinerary. However, all guests must include their eligible frequent flyer number on their reservation prior to check-in to access the lounge. oneworld® frequent flyer membership cards do not grant access to the lounge and the frequent flyer number on the reservation will determine whether a member is eligible for access.'I haven’t been able to access all the info I heard from the agents yet.
What she is citing to you is the access policy for class of travel (ie first class), not for elite status.