I’d like to point out that while some things about the assassination of MLK don’t add up, conspiracy theories don’t agree about exactly who was behind the assassination. A civil case in 1999 pointed to the Mafia and Nashville law enforcement, for example.
Although there isn’t sufficient evidence, I think, to draw a solid conclusion about any of these theories, I don’t think they are outside the realm of plausibility.
As threatened as racists in power were by MLK, it isn’t a huge stretch to imagine one of the more corrupt ones going farther than simply attempting to discredit him or push him to suicide, since those tactics didn’t work.