There is no rule, anywhere, that states that you need a CDL to operate a vehicle with air brakes.
That's true, but for some reason, if you need a CDL, you need to pass the air brake part of the test if you drive with them. If you have a truck with air brakes but not heavy enough to require a CDL, you don't need to get one because of the brakes.
I wonder who came up with that rule.