Draft resistance was really bad during the Vietnam War. There was a lot of opposition to the war, the war was seen as pointless, it seemed like a bad situation fighting in the jungle etc. About 30,000 went to Canada and there were legal ways to avoid Vietnam.
The upper crust had lost interest in military careers. Word probably got around that being a platoon or company commander in Vietnam was particularly dangerous. There were officers "fragged" by their own men, and it was a difficult with discipline not strong, not being able to easily tell civilians from combatants, etc.
So the wealthy and the powerful (mod edit) used money or connections to avoid that.