This is at most a conflation, not a misconstrual.

I prefer to think of these words as points in a spectrum, rather than definitional prisons with tight boundaries.

Allowing school districts to do what they are constituted to do, is more democratic than delegating it to the State governments, which is more authoritarian.

Authoritarian is also not an antonym of democratic. They correlate, but not as strongly as any advocate for democracy would prefer.