Is it possible NatWest are getting confused with their own online banking screen, which does just what you say and asks you to enter 3 letters from your password:
Your NatWest password should not be the same as the Verified by Visa one (unless of course you set them both to be the same thing).
I have used sites all over the net that use the Verified by Visa scheme and they have
always asked me for the full password.
This is an example of the screen I assume you're seeing:
Hope this helps,
James.