Another thing to be aware of, is projects include items in the build queues.
I had a similiar problem trying to build a Spaceship Engine, which is a One Project build. City X was going to take 36 turns to build, whereas my Capital could build it in 12 turns. I set City X to build something else instead, but the Engine was still grayed out when I tried to set my Capital to build it. Domestic Advisor didn't show any other cities building it. Going back to City X I saw that the Engine was 2nd up in its build queue. Once I removed it there, it became avail in my Capital.