He said the right thing at the right time. And when he wanted LBJs support, he said he supported LBJ.
You seem to think MLK never spoke again after writing the letter you cite over and over.
Do you even know who MLK openly supported in the 1964 election?
Nationwide and statewide. She leads in a majority of swing states.
And you win the election by winning swing states, not necessarily the previously uncommitted.