I learned something on a recent trip that I didn't know. When (as a former US DM member) we were part of *A, I was under the impression that being Gold or better allowed me access to overseas *A lounges regardless of what carrier I was flying with.

But recently, I went into the 1W contract lounge in MXP having flown in on AA and flying out on TK, they would not let me in even though I had arrived on a 1W flight. Am I correct that this is a difference between the two alliances?