LBJ was a guy that deeply cared about his legacy and was troubled in the last years of his life that this war pretty much erased away all the good he did (in the early 70's). So, it's not surprising to me that people whose job it is to preserve his legacy would float this out there in an attempt to influence history.
It's not like Nixon was alone in benefitting from the war going on a bit longer. The entire industrial/military complex was always convinced they could win that war if just given more men and more ability to strike outside of the parameters they were given. Still to this day that argument echoes. So, I think it's a bit presumptive to assume that this woman held enough sway to derail these talks by herself. Especially in that era where women were held in much lower regard than they are today.