Do oneworld Sapphires and Emeralds flying with Iberia have access to the Prime Class Lounge at IST?

I assumed that they do as the oneworld website seems to suggest this as well as the Iberia Lounge thread here on Flyertalk. Despite this I had a bit of a fight getting in. 2 agents at the desk looked very confused and said that I needed a BA boarding pass (I guess because I handed over my BAEC card). When I said I was travelling with Iberia they still said that they needed to see a BA boarding pass and then asked me if it's the same company! I needed to be a bit forceful and politely argued that the oneworld website indicates I should have access. A supervisor was called and she said that although they weren't sure, I could enter. They made me feel like they were doing me a favour! Were they?!

The lounge is actually very good and they have a nice selection of hot food and cakes. I had 3 pieces of cheesecake which was the best I've ever had in an airport lounge.

A related issue was that I was refused Fast Track security as they said I'd have to be travelling business class. The sign showed the Iberia logo so I think the agents there need to brush up on access rules too!