What about "Joe has, at the time this sign was made, never denied beating his wife on Decemeber 31st." The claim could be very true in that Joe never has denied that specific claim because there was no reason to deny a claim that hadn't been made yet.
What about putting up the sordid details of a teenagers love life on a bulletin board outside her high school? Assume you verified the statements as factual. Is there perhaps an issue even when it is the truth?