We are talking *primary* here. And yes it is sort of like "give me a Democrat or Republican ballot because I'm not registered in either party." The worker gives them whatever ballot is necessary and a chip that is either red (for Dem) or blue (for Repub). The voters show whatever colored chip is necessary, then "vote" in the primary and then they return the colored chip to the workers and get to walk out "undecided" again.
Bene--the folks say that they are *not* registered in any party and there is no way to check if that's true or not. Heck, even people that had been dead for six years voted in the last election!
That's partially the reason folks want voters to show picture I.D. (my children used to have to have that just to go to school and I know that people need that to collect foodstamps and welfare as well) before being able to vote.