Can Cheney declassify documents?

In the interview with Fox News about his shooting incident, Dick Cheney made the following claim : There is an executive order that specifies who has classification authority, and obviously focuses first and foremost on the President, but also includes the Vice President. From what I can tell, the Executive Order he is referring to is 12958 . It talks about the classification and declassification of documents, but as far as I can tell, there is nothing in it that gives the Vice President any power to declassify documents. This is held by the President, Agency heads, and the Archivist at the National Archives, as far as I can tell. The section relating to declassification is Part 3.

UPDATE: John Dean was asked about this and said that he did not remember an executive order that allowed the Vice President to unilaterally declassify documents.