Iam not so sure.
I have read several places that LBJ hated the Kennedys.
LBJ had to do a lot of arm twisting (which he was known for) to get both bills passed.
If JFK was still president would LBJ have worked hard to push those bills through?
Sure seems like a lot of speculation about Democratic politics of the time, would a veep go to war against his president fighting an issue they both wanted, seems like a lot of unnecessary searching for something just to protect the never ending myth making of one of the sleaziest American presidents of all time.