In Errand of Mercy, Kirk informs Kor that the federation is a "democracy."
But (as previously noted) democracy can take many forms, so while the federation council might operate as a simply democracy, one vote per member, or one vote per species, the various member star systems could have a wide variety of government types. Ardana obviously wasn't a democracy, but is
a federation member in good standing.
Kirk can even recite parts of the Constitution!
Kirk was from iowa, an American state, so while he could recite the constitution of the land of his birth, could Kirk have recited the equivalent document from another nation on Earth, or from another planet?
Actual make a certain amount of sense. Right from the first pilot, we see alien cultures being able to access the Enterprise's computers, keeping some information (obviously not all) physically separate from the computer on individual drives ("tapes") would prevent them from being casually read if the computers aboard the Enterprise were to be hacked.
In TNG and VOY, look how often information is physically walk around the ship on handheld Padds, instead of being messaged electronically.