Yea, that threw me off. I'm not sure exactly what is going on there. I do see that Reca/Peca did not seem to advance that far in rank, even in wartime. My guess is that he got himself in trouble, more than once. That does mix with what we know about his background.
Lisa (his niece) posted some of these docs on Facebook. She did acknowledge that the CIA thing may be a little far fetched. Those docs did have a certificate of graduation from the Army Airborne school, and a pic of Reca with his jump wings on. The previous pictures may simply have been before he got his wings.
What was not in those files is a DD214, which is a record of discharge and lists information regarding his overseas service, awards, etc. It is not a comprehensive list of everything he did, but it tells a lot. Back in the 1950s it may have had a different name.
I would like to see if he did make it over to Korea during the war, and how long he actually served in Airborne units. Based off the insignia in one of the photos, it looks like he was Infantry. Given that his first discharge was in 1954, he falls into the over 63 years from discharge, and therefore anyone can get his military records. However, if they count his National Guard time and Air Force Reserve time in that calculation, they may not provide the information.
My initial assessment is that Reca served a few years in the Army, jumped out of planes, then left the service, went into the Air Force Reserve, was activated for a month or so, then went back to weekend duty. He would have had the skills to jump out of a 727, and the balls. However, nothing in his background indicates that he was CIA or a secret agent, etc. He was a storyteller, and it sounds like he was a good one. He's a guy I'd like to have had a beer with, but with his blue eyes and stories, I don't see him as Cooper.