That's where a lot of the confusion comes in: The DD 214 doesn't say, specifically, where you served, only when, so us "-era vets" can get by with the deceit.
When I was at the license bureau (Colorado) with my DD214,they were all set to issue me "Vietnam Veteran" plates until I insisted on the "Honorably Discharged Veteran" plates. The clerk was a little confused about the distinction.