I'd like to side step the history of where this idea came from, and hopefully someone else can provide a specific answer to that.

I would however like to repost an answer I wrote on the specific question as to whether it was true that the US never lost a battle in Vietnam, which is a claim that occasionally comes up.

It is definitely true that in almost all military engagements, the US military inflicted higher casualties on the FLN (Viet Cong) and NVA (North Vietnamese Army) than it received. But this alone does not make a "victory" - to pick an example from the First Indochina War, Viet Minh casualties in the Battle of Dien Bien Phu were much higher than those among defending French forces, but this was a decisive French defeat.

It is also true that most military engagements in the war saw the US also gain a tactical advantage. But there were exceptions. One notable example is the Battle of Ia Drang, fought in November 1965. The article cited here by Stephen M. Leonard notes that this was a search-and-destory mission conducted by elements of the 1st Air Cavalry Division, which Brigadier General Richard Knowles (the assistant division commander) himself described as “based on strong instincts and flimsy intelligence.” Without getting into the battle's details, the purpose of this mission was thwarted, US forces were attacked by the NVA and engaged in a "fight for survival" to secure their landing zones. While the NVA suffered far higher casualties than US forces, they managed to consistently maintain the offensive, including ambushing US forces at Landing Zone Albany and inflicting 279 casualties, leading Leonard to write "Inevitably, there were those who would draw comparison to Custer’s 7th Cavalry at the Little Big Horn." Note that this is more-or-less the official US Army version of the battle, so that at best one could say that this engagement was a costly draw, at worst a defeat for US forces. This is the engagement that features in Harold Moore and Joseph Galloway's We Were Soldiers Once ... And Young which was adapted into a 2002 film by Mel Gibson.

Another engagement that was major and more clearly a defeat for US forces was the Battle for Fire Support Base Ripcord in July 1970. This battle is much less well-known than Ia Drang, but involved elements of the 101 Airborne Division being attacked by the NVA at a fire base near the Demilitarized Zone. After a 23 day battle, the US forces withdrew from the fire support base.

As noted in the Politifact article, these are just more clear-cut examples of, if not defeats, "non-wins". But even in cases where US forces arguably gained tactical victories, such as the Battle of Hamburger Hill in May 1969 (US forces obtained their tactical objective and inflicted high casualties on the NVA), the hill in question was abandoned days later, and officials in the Nixon administration considered it a Pyrrhic victory which could undermine support for US involvement in the war. So in this case - a "victory"? Or not? Or both?

Even in larger cases, such as the Tet Offensive, victory is not clear cut. To pass on a quote from historian James Bradford, via Politfact:

""It was a tactical victory for the U.S. in the sense of casualties inflicted and a strategic victory in the military sense, because it defeated the enemy's plan in the field ... But the North Vietnamese won a strategic political victory in the sense that the campaign eroded support for the war in the U.S. and contributed directly to President Lyndon B. Johnson's decision to not seek re-election."

So in this sense, the Tet Offensive was a significant defeat for North Vietnam in terms of its immediate military and political objectives - the US was not defeated in a set-piece battle at Khe Sanh, FLN cadres were largely destroyed in the fighting, and the FLN did not manage to ignite a country-wide revolution in South Vietnam. But the offensive undermined already weakening (as I discuss here) US political and public support for involvement in the war, ultimately forced a US president from office, and brought the US to the negotiating table in Paris. So again, what is a "defeat" and what is a "victory"?