The way I read this is that the state requires proof of citizenship before you’re allowed to vote in state elections.
But you’re on the honor system for Federal elections.
Not sure if this is because of past legal rulings or what.
Small point, but by definition it's only non-citizens that are on the "honor system"...and what reason is there to think they care especially if they have been told its Ok, or perhaps even picked up a few dollars for voting?