Generally speaking, modern defamation law applies only to false statements; but at some point a literally true statement may so strongly carry a false connotation that the speaker could be held liable for the implied falsehood despite the literal truth. I've often looked for a good example of this, and I just found one, in an early 1960s case (though it's been around outside the defamation context at least since 1916): The first mate who, upset by his teetotaling captain, writes in the ship's log,
Captain sober today.
H.P. Grice's work on conversational implicatures, by the way relates to this.