Perhaps they misspoke, or perhaps they misunderstood, or perhaps their usage of the term is different then yours or mine. I understood them to mean it in the sense that the FDA holds democratic legitimacy by nature of its assistance as an org within the US government, which is by any reasonable definition a democratic institution.
The point is that its not really relevant to the point they are making, which is that the FDA as an institution has some weird incentives.
> motte-and-bailey.
I'm not familiar with this idiom so I cant say.