Interesting.

I did once have a time where the agent tried to tell me P=0 even though EF told me P=1. She told me that EF wasn't up to date. I told her I could also purchase a P fare on the website. She told me it was phantom availability, the website didn't have the latest inventory (she said the same of EF) and that it would error out before I could purchase. So I purchased it, it went through, and she agreed to go talk to NRD. After talking to them for a bit, they figured it out and got the upgrade done. I don't know exactly what they did, but it worked out, which was all that mattered to me.

Have you tried to see whether you can actually purchase the flight in question in P?