They're confused alright. Some of the people attacking the FSP think they aren't democrats.
"D(d)emocracy and liberty are often thought to be the same thing, but they are not. D(d)emocracy means that people ought to be able to vote for public officials in fair elections, and make most political decisions by majority rule. Liberty, on the other hand, means that even in a democracy, individuals have rights that no majority should be able to take away."
- The Bill of Rights, A Brief History
“Democracy is the theory that the common people know what they want, and deserve to get it good and hard.”
H.L. Mencken