When a rumor goes around about a friend, “that doesn’t sound like them” is a full defense.

Rumours need agreement to travel. Each person who hears one makes a decision about whether to pass it on, and most pass it on because nobody in the chain pushed back and silence reads as agreement. Four flat words from somebody who knows the person breaks the chain, because the story now has a cost to repeating. You do not have to prove anything, only decline to carry it.

Say your version of it the next time something goes around, calmly, without a speech. Then do not ask the subject about it, which only tells them it is circulating. And tell them later only if they would want to know.