This. I’m a decade+ younger than this thread’s poll voters, but I remember very clearly that the kerfuffles about “draft dodging” were about doing illegal stuff to get out of serving: draft evasion. Getting a student deferment or a National Guard appointment, etc., was not “dodgy” because it was legal: draft avoidance.
I would quibble that what did a lot to shift the popular perception of the meaning of “draft dodging” was not so much “valuing military service” in the abstract, but rather Republican rhetoric during Bill Clinton’s Presidential campaign in the early '90s. A lot of people were suddenly denouncing a Vietnam-era student deferment as “draft dodging”, and thereby conflating it with illegal evasion such as fleeing to Canada or faking papers, which back in the day were seen as very different.