/u/Bernardito has an answer for you

The phenomenon of vets being spit on seems to be largely anecdotal so I'm not sure I can faithfully speak to its veracity. However, the mistreatment of Vietnam veterans is a bit more complicated. As Chrisitan Appy writes in Working-Class War: American Combat Soldiers and Vietnam, this mistreatment generally did not manifest itself in "explicit acts of hostility but quieter, sometimes more devastating forms of withdrawal, suspicion, and indifference." Mistreatment of vets, more often than not, seemed to be a lack of respect or recognition. As much of the American public perceived the war as a failure, there existed a general desire to "forget" the war. Vietnam veterans were often unwelcome at Veterans Day parades. Numerous first-hand accounts echo the idea that vets were "forgotten."

In the 1986 Veterans Day ceremony at the Vietnam Memorial, one speaker argued against a perception that "the cause for which we fought was not worthy of your lives." Another speaker noted, "For a long time we were forgotten. But now we are not forgotten, we have our memorial, we've had our parades." Likewise, at the 1985 ceremony at the Vietnam Veterans Memorial in New York, Mayor Koch calls the lack of previous recognition for Vietnam vets a "terrible injustice" and refers to Vietnam veterans as a "lost generation."

While outright harassment of Vietnam veterans almost certainly did happen, mistreatment of Vietnam veterans was usually a lack of recognition-- a perceived amnesia about the sacrifices made by veterans. In short, your friend's claim that veterans' mistreatment is a "myth" is misleading at best.

Sources:

• Appy, Christian G. Working-class war: American combat soldiers and Vietnam. Chapel Hill, N.C: U of North Carolina Press, 1993. Print.

• Franklin, Ben A. "VIETNAM IS A FOCUS FOR VETERANS DAY." New York Times n.d.: n. pag. New York Times. Web.

• Gross, Jane. "NEW YORK PAYS HOMAGE TO VIETNAM VETERANS." New York Times 7 May 1985: n. pag. Web.