That's odd. Since I moved to Gib, I've changed my contact details with Natwest to a Gibraltar address and telephone number and they were fine with it.
When I went to the Natwest here, they did say that they operate separately. But they have authority to carry out certain processes on behalf of Natwest UK, such as security document review and internal mail.
I have heard that there is a waiting list for a Natwest account, but it's probably not as long as the waiting list at most other local banks. Some of the banks here will only take you on if you are depositing £xm. When I was in the local branch, they asked me if I wanted to apply for a Natwest Gibraltar account, so I got the impression that the waiting list couldn't be that long.