It was confusing because certain oneWorld carriers permit their own Emerald level members to use their lounge and if another airline's Emerald level member shows up, they are quite lenient.

When in SYD a few months back, I was flying Thai on an award ticket, QANTAS permitted me to use their Qantas Club lounge plus my travelling companion.

When I was in BKK, I used the CX Business Class lounge when I was travelling on Scandinavian Airlines (the aircraft's gate was closer to the CX lounge than SAS's).

As tedhl mentioned, yes, Cathay permits their Diamond (1w-EM)to use the Biz class lounge when flying another airline. So maybe this was why.