It seems to me that you are failing to understand the word “reciprocity,” here.
It means the following (quoted from the EO):
Sec. 4. Reciprocal Recognition of Fitness and Suitability Determinations. (a) Except as provided by subsection (b) of this section, agencies making fitness determinations shall grant reciprocal recognition to a prior favorable fitness or suitability determination when:
blah, blah, blah
Read the EO itself for the details, it’s very easy to read amd less than a page. Google “Bush Executive Orders” and it will be the first listed. Or follow the link in my original post.