Ah no; we would have been in it a lot sooner if that were case, having committed up front to keeping it free from Soviet attempts to collapse it.
Johnson did what anybody else would have done in the same situation, i.e. where his entire JCS and his own Secretaries were ally lying about the facts, and trusted none of them, so he took control of some facets of the war himself. He wasn't going to be led into criminal acts in violation of the UN mandates by his political enemies, either. IT was the press who made TET, a major and final defeat of the Viet Cong, look like a major victory, and it was also the press who never complained about the North's constant violations of UN restrictions ignoring the DMZ and their use of the trails in Laos and Cambodia. You can blame the press and the pseudo-intellectual commie in American academia for selling the public bullshit about the 'war' that continues to this day. It was right for the U.S. to get involved, same as it was to get involved in Korea, the ME, Africa, and South America. The difference between Johnson's escalations and Eisenhower's wimpiness and conservative approach to the Cold War is like night and day; Eisenhower rescued no one from Soviet and Red Chinese mass murders and slavery, Johnson's polices bankrupted the Soviets' imperialist dreams and kept Red China and the Soviets divided, and pretty much ended the Cold War. Nixon merely reaped the benefits of a bankrupt Soviet Union.