Will an Apple Watch 3 purchased at AT&T work on Verizon, and if so, why does Verizon say it can’t be used?

Let me be more clear - Verizon states I CANNOT set up my watch (originally purchased outright - not on a payment plan - from AT&T) on their network, and that I need to buy a new watch that IS compatible. According to MULTIPLE Verizon reps, both in sales and in their tech support departments, the Apple Watch 3 I have now is not compatible on their network. Is this now an expensive paperweight because Apple and Verizon want nothing more than money?!