They did, I agree.The fb0 did slander him badly. Just like Trump.
BUT we are not talking about the FBI. We ate talking about MLK Jr.'s explanations of his faith.
He preached the empty tomb and undying Christ. But he explained this (apart from the pulpit) as outward expressions of inner experiences.
Those ho followed Christ eorehis death were drawn to his personality. They found God (this higher ethical existance...good conquering evil) in Christ. When Jesus died this truth (this "god") lived on in them rather than dying with Christ.
MLK's explanations is that in a pre-scientific age these inner experiences found an outward expression in the myth of a bodily resurrection, virgin birth, and divine Christ.
But if you strip away what we know is false (the supernatural) you arrive at the foundation. The grave was empty (the ethical philosophy of Jesus did not die with the man).
I'm sorry, but that is NOT Christianity any more than the Jefferson Bible is Christian.