i will ask my old NASA buddies about this and see what they say.
This make pretty good sense though.
Here are a couple of things from the internet that might help explain this...
Lt. Col. Arminta Harness blazed a trail for women engineers in the Armed Forces during her 24 year career in the U.S. Air Force. Graduating with an aeronautical engineering degree from the University of Southern California in 1955, she became the Air Force's first woman engineer, rising to the rank of Lieutenant Colonel. Her assignments varied in responsibility from designing intelligence-gathering equipment for the U-2 aircraft to providing management direction for the $2 billion Space and Missile Systems Organization budget.
As a lieutenant assigned to the Aerial Reconnaissance Laboratory at Wright Paterson Air Force Base, she was the first woman on orders as a test engineer during flight testing of experimental equipment, which she designed. In 1963 Harness was assigned to work on the Gemini manned space program at Air Force Space Systems. As a Major, she served as Deputy Chief of Engineering, and later, as Lieutenant Colonel, as Chief of Program Control for the $80 million Gemini Target Vehicle Program the unmanned spacecraft used as a docking target by the Gemini astronauts in space. It was during this assignment that she became the first woman to receive the specialty rating of Staff Development Engineer and the first woman to receive both Senior and Master Missileman Badges.
In August 1963 General [John B.] Hudson returned to the ballistic missile and space program in Los Angeles, where he became assistant deputy for engineering and later deputy for launch vehicles, Space Systems Division. He was awarded his third Legion of Merit and earned his Master Missileman Badge for directing the launch vehicle activities of the Air Force space program. In this assignment he was responsible for developing launch vehicles and space vehicles used by the Air Force and NASA, such as the Scout, Thor, Atlas, Titan II Gemini launch vehicle, Agena, and the Gemini Agena used to rendezvous, dock and maneuver by Gemini astronauts.
Interestingly enough, I don't find any mention on the internet of Tom Stafford or Jim McDivitt being awarded the Missileman Badge.