The following information has been provided in great part through the courtesy of Clark Ketter, web master and historian of the 3084th Aviation Depot Group at Stony Brook.
Two months prior to my seperation from the 814th CDS 22 June 1962, "A" Flight of the 814th CDS moved from our barracks on Westover out to the barracks on the grounds of the 3084 APS at Stony Brook. At the time, it was thought that this move was to provide needed barracks space for incoming, new 814th CDS 77130's. But that wasn't the only rumor floating around. No one really knew the primary reason, or if they did no one was talking. It was interesting. One day we couldn't approach any closer than X number of feet to the main gate of Stony Brook; and the next day we were billeted there, and our line badge was good enough to gain entrance and go to our barracks. I believe we still took our meals at the 24-hour Mess at Westover, but all our gear and personal items were out at Stony Brook. If anyone can add to or correct this, it would be greatly appreciated. I am specifically interested as what happened to the 3084th APS. You can contact me here.
In any event, information from Clark has cleared up the rationale for the 814th CDS's move out to Stony Brook. In a "Summary History Statement" provided by Clark Ketter from the USAF Historical Studies Branch, USAF Historical Division, to Clark, we have the following statement:
"On 1 July 1962 this station was transferred from the jurisdiction of AFLC to SAC." This document can be viewed here.
The referenced "Station" was the 3084th Aviation Depot Group. So, on 1 July 1962, SAC assumed responsibility for Stony Brook. However, the Stony Brook 3097th ADS, AFLC still maintained its responsibility regarding the maintenance and care of all nuclear, thermonuclear and conventional devices. It is also now apparent why then Capt. Frank Hoffman (now Lt. Col., Ret.) was transferred from Stony Brook and the AFLC back into SAC and appointed Squadron Commander of the 814th CDS, as he had experience with both the operations of Stony Brook and SAC's CDS.