I think the CIA's assassination of Diem really was the decisive event that solidified our presence there, and that was under Kennedy's hand.
It's noteworthy to look at the roles of the secretary of state and George Ball had in the decision making process. I can't believe I'm blanking on the sec'ys name, but his opinion was the polar opposite of Ball's, which stated, correctly, that increased military action would only make shit worse.
Johnson kept trying to convince people that the blame of Vietnam really belongs on Kennedy, even to his death.
Also, consider that it would've been a political nightmare for Johnson had he just pulled out and Vietnam went to the north. It was either that blatant reality, or the gamble of putting more forces in to try and save it.