Rumors you repeat carry your name on them now.

Repeating something makes you a source. The next person does not carry it as something a stranger said, they carry it as something you said, and if it falls apart, your name is the one attached. The original teller gets no part of that. What you got in exchange was a few seconds of being interesting.

When something arrives about somebody, let it stop with you, which mostly means saying nothing rather than saying anything clever. If you find yourself about to pass it on, ask whether you would say it with them standing there. Being the person a story dies with is a quiet reputation worth having.