The strongest answer to a rumor is one boring, true sentence. Then stop talking about it.
LEADERSHIP
LEADERSHIP
A long denial gives a story more to feed on. Every detail you add is another line to be quoted, argued with and passed around, and the heat in your response is what makes it worth repeating. One flat, true sentence is unsatisfying, which is precisely why it works. Boredom kills gossip faster than outrage ever has.
If something is going round about you, pick the single true sentence and say it once to whoever needs to hear it. Then get on with your week. Not explaining again is the hard part, and it is most of the method.
Could you answer a rumor in one dull, true sentence?
Free, with nothing to buy inside it.