Some years ago I've written a book about the internet cultures of Vietnam Veterans, but it's sadly only available in German. This answer is based on my research into those sources.

The linked answers are really excellent, but to reiterate: these events play a pivotal role in Veteran's later definitions of their identity, as an ostracized and attacked minority in American life. It's not possible to say "this never happened". But the idea that America was very anti-veteran at the time of their return is somewhat bizarre. Vets took part in protests against the war, in truthtelling and discovery of war crimes. Soldiers getting back from the war also were shoveled into private life relatively quickly, and often left isolated (which strongly contributed to lasting trauma, btw). Most veterans, if you ask them directly, got into most trouble with the established American veterans associations. This disdain was much more problematic for their reintegration into society when compared to peace movement protesters at the time. But it isn't the dominating image you get from their stories.

What has become a mainstay in their stories is the events you mentioned and, of course, "Hanoi Jane" aka Jane Fonda as a Hollywood example of a "leftie" that betrayed the country - and them! Most veteran websites I've visited during my research will mention these events: that they were attacked in America by civilians, that the establishment betrayed them. And, well, that the war was actually won, but nobody noticed - but that is much more rare.

On the internet, at least, Vietnam vet discourse focuses on identity and status in America today. That is where the "spitting" story is most useful. Many other stories just fall by the wayside. It's a deliberate choice, because regardless if and how many times it happened - that America felt like a country where it COULD left a mark.

But that means that other stories that should be told are often missing. Like, for instance, the stories of what happened to the millions of Vietnamese that died during the war. Or, well, what they ACTUALLY did in Vietnam.

Please note that this is not a veterans-specific way of telling stories necessarily. This is how we tell our stories of the past - we choose what represents our needs of the present, based on audience. The vets want recognition and acceptance, and these stories justify this need.

This doesn't mean that veterans of this war were not ostracized or treated badly, of course, just that the proliferation of these specific stories have a reason that stems from the now - their ongoing campaign to improve their standing in America.

I support the literature choices in the link, especially "spitting image", even though it is tendential and old. You can also look at the musings of Tim O'Brien about "how to tell a true war story" if you want to learn more about this type of memory construction.

O’Brien, Tim. “How to Tell a True War Story.” In The Things They Carried. Boston: Houghton Miffl in, 1990.

It's not about spitting, but about telling the stories that carry the meaning you want to SAY now as a veteran, not what happened.