FALSE, and badly so, but you have to read the history and look at the actual timeline.
Full Disclosure: I am cribbing heavily from Jerry Pournelle's writings in this.
First, it is necessary to recognize that there were in fact THREE wars being fought in Vietnam in the 1960s and early 1970s.
The first was a revolt-from-within in South Vietnam, by the Viet Cong. The Viet Cong LOST that war in 1968: the Tet Offensive was their absolute last gasp. They were losing, they knew it, and the went for broke. They threw everything they had, including every kitchen sink and chamber pot they could find, at the US Army. The Army took it all, soaked it up, shook it off, and said, essentially "Is that the best you can do?" The VC were never a factor again in the hostilities after Tet. They were done.
The second was a conventional land grab from North Vietnam, that had been flaring up periodically for some two thousand years, that usually fought itself to a standstill at about the DMZ. The VC made common cause with the North Vietnamese Army, who saw a chance to use a proxy to weaken the Army of the Republic of (South) Vietnam. Once the VC were off the board, the NVA continued the fight.
The US essentially won that war, and withdrew from Vietnam in 1972, leaving only a commitment to provide air cover when needed. With air cover, the ARVN was quite capable of handling the NVA, and did so, handily. This included making Brillo (Tm) pads out of a larger mechanized army than Hitler's Germany ever fielded. Two years later, while hounding Richard Nixon out of the White House, the Democratic Party reneged on the air cover pledge, and South Vietnam fell. The US didn't lose; the Democrats THREW THE VICTORY AWAY.
The third war is the interesting one. Vietnam was not just a stand-alone war: it was a critical campaign of attrition in the Seventy Years War between the United States of America and the Union of Soviet Socialist Republics. In such a campaign, the trick is NOT TO WIN OUTRIGHT, but rather to keep the other guy thinking that he can win it if just commits some more resources to the meatgrinder. The object is to cost the other guy a lot more than he costs you, and, in this regard, the US was howlingly successful in Vietnam. When Vietnam finally fell, the next campaign was in Afghanistan, where all the US did was supply Stinger SAMs to the Afghans, depriving the Soviets of their air cover assets, and letting them learn why nobody in their right minds EVER gets into a serious fight with the Afghans.
Bluntly, the US did not "lose" the Vietnam War. By any sensible set of victory conditions, the US won. The problem is that the Democrats then betrayed South Vietnam, and let them fall.