I purchased a last minute ticket on United's Japanese website for a codeshare Turkish Airlines flight that was under the left-most economy tab but said in Japanese "First Class (Flexible)." It was expensive so I assumed that it would actually be first class. On the actual ticket, it said "Fare class: First (A)" but when I checked in, both Turkish Air and United told me that that must be a mistake and that I was actually flying economy.

I still got to take my flight, but I'm pretty upset that I could have taken a cheaper flight for the same experience. Any thoughts on what First (A) means and whether I am wrong or right?

Attached is a screenshot of the ticket, which was sent in English.