What they said was the Watch would have to be on the same carrier as the phone and that it would share the same phone number. The presumption of course is that it would have to be with the same account holder.
The Watch will have its own account and a separate built-in electronic SIM. Whether or not you could have it tied to a phone on another account remains to be seen. I see it as the equivalent of buying the Watch without a phone and setting up an account for it with your carrier of choice. It just doesn't seem like a carrier would do that.
The carrier should be able to advise, but I've found too many reps weren't knowledgeable on odd details in early days.