I've never taken a "puppy kindergarten" class, but all of the Obedience classes I've ever signed up for with an adult dog, give people the option to show up with the dog on a flat buckle or choker-style collar.
Most trainers I know start off from scratch with everybody on a buckle collar & modify their approach for each individual dog, based on behavior patterns & problems that arise. All dogs are different & a trainer simply can't expect one approach to work for all the dogs in a group class!
In any given group you're bound to have dogs like Basenjis who resist & shut down when given harsh corrections….and high-drive, hard headed working-type dogs who respond to praise BUT also benefit from a well timed collar correction. You won't get anywhere trying to train a Basenji with the same methods you'd use with a Ring sport Malinois....
Personally, if I ever decided to use a "correction" collar on any dog, it'd be a prong collar. It's just about the only tool that REALLY helped me work with my Boxer & her over-reactive issues. Properly fitted & properly used, a prong only requires light "fingertip" corrections and is actually easier on the dog's trachea than a "choke" collar.
However, I wouldn't choose to use ANY "correction collar" on a Basenji....and wouldn't enroll my pups in a class that required their use. JMO