I have been using Final Cut Pro for years and years, and never came across of this problem. I always use downloaded fonts, (.TTF) and they always used to work perfectly in Final Cut.
I am using Final Cut Pro 07, and the fonts used to show up all the time, but now, suddenly, they all disappeared from ALL the texts in FCP. They work everywhere except for FCP. They work in Microsoft, TextEdit, AE, PhotoShop, etc. but not in final cut pro.