This isn’t quite true. Under Clinton v. Jones, to be protected, the president’s statements have to fall within the “outer perimeter” of his official responsibilities. It’s hard to see how these statements have anything to do with presidential duties.
In the Clinton case itself, the last claim of Jones’s complaint asserted that he had defamed her by having White House staff deny that he sexually harassed her. The Court didn’t decide whether Clinton was protected from that claim. 
Even if you assume that a president’s official responsibilities cover denying accusations of personal misconduct made against him, which is debatable, it’s hard to see how they could include making a baseless murder charge against a TV personality the president doesn’t like.
