As I understand it, the person to determine how the VP is covered under the Executive Order is....surprise, the AG, Alberto Gonzales.
....the National Archives wrote to Attorney General Alberto Gonzales in January 2007 to seek a resolution of the impasse. The Vice President’s staff responded by seeking to abolish the agency within the Archives that is responsible for implementing the President’s executive order.
http://www.speaker.gov/blog/?p=507
Six months later, the AG has still not responded to the letter from the National Archives....I guess he's been kinda busy...or he forgot (oh that faulty memory).
This does have the making of a serious constitutional confrontation.