You are correct, sir.
http://www.koreanwar-educator.org/
Search for, national guard
The list of units that served including whole divisions is from "When Are We Going? The Army National Guard and the Korean War, 1950-53," authored by Renee Hylton.
We know about current NG and reserves service.
Why was Vietnam an exception? To the best of my knowledge LBJ feared that activation would disrupt his plans for his "Great Society" legislation but I do not recall that his administration ever stated publicly that they would never activate the reserves.
I don't know how much trouble it was to get into the Guard during the Vietnam war but in the 1950s six years' service in the Guard was a way of avoiding the two-year peacetime draft -- but it was not considered to be a way of avoiding combat in case of war.
Those going after the President are making a big mistake trashing the reserves.