The FSF has never claimed that the GFDL is a free software license.
You are correct that the OSI and the FSF have different goals, they also have different criterias. The NASA Open Agreement fails the criterias for free software. And the accepted definition of free software is the one set by the FSF, and has been in use for more than 20 years now. It is also the definition used by FSF Europe, and the rest of the free software community. In the end, the OSI also includes lciensesicenses that are deemed non-free software, since they have criterias that are not as strong as the free software ones.