This is absolutely not true. I never traded a phone in to start a JOD contract. it is not REQUIRED to trade in a device to add JOD.
Correct, but if you pay off the device that would remove the current JOD (how it was explained to me). Therefore, you would need to add JOD again. Hence the trade in.
Edit: I read the last part of your post wrong. It is required to trade in a fully paid off device to add JOD for the first time. We had to do it on all 5 of our lines. All done at different times. Some in store and some over the phone.