While I appreciate that he wasn't a COMBAT vet and you may question the vet classification in association with a war period from your stance, for veteran benefits purposes, here's what the VA says:
https://www.benefits.va.gov/pension/wartimeperiod.asp
FTA:
Eligible Wartime Periods
Under current law, VA recognizes the following wartime periods to determine eligibility for VA Pension benefits:
Mexican Border Period (May 9, 1916 – April 5, 1917 for Veterans who served in Mexico, on its borders, or adjacent waters)
World War I (April 6, 1917 – November 11, 1918)
World War II (December 7, 1941 – December 31, 1946)
Korean conflict (June 27, 1950 – January 31, 1955)
Vietnam era (February 28, 1961 – May 7, 1975 for Veterans who served in the Republic of Vietnam during that period; otherwise August 5, 1964 – May 7, 1975) [my emphasis]
Gulf War (August 2, 1990 – through a future date to be set by law or Presidential Proclamation)
My father was stationed in Europe during his five-year stint in the US Air Force as a volunteer, from roughly 1960-1965. Never set foot in Vietnam. Upon his death, he received the following type of grave marker from the VA/National Cemetery Association that was placed on his burial site:
which specifically listed his rank and states VIETNAM on the plaque. Whether folks want to call a Vietnam vet someone who saw combat duty, or was stationed in the theater, or "in the rear with the gear," or who was in the services somewhere on the planet during war-time at veteran, that's of their own choosing, but someone who served in the armed services is a veteran regardless of war-time or peace-time or "ceasefire" time or humanitarian aid time. Someone who served in the services during the designated periods are considered veterans of that war ... with the exceptions listed above such as the early part of Vietnam or the Mexican Border Period.
I would hope that we'd all, especially those of us who have or have had service members, don't get caught up in playing "he's not really a vet." You can make the claim that he's not a combat vet, but he's a vet nonetheless. And by the limitations provided by the VA ... for example, you had to have been "in-country" to be counted as Vietnam vet from February 28, 1961 - August 4, 1964 or in the service, August 5, 1964 - May 7, 1975 ... they have already accounted for the fact that "in-country" isn't a requirement for classification of a Vietnam vet unless it was in the February 28, 1961 - August 4, 1964 period.