It’s the phrasing that intrigues me, “you will save both yourself and your hearers” because similar phrasing turns up in other writings ($af(2Cl 15.1), $af(IEph 16.1-2)) as well.
Here’s what I found in Hermas, Mandates 2.2 (27.2):
First, speak evil of no one, and do not enjoy listening to someone who does. Otherwise you, the listener, will be responsible for the sin of the one speaking evil, if you believe the slander which you have heard, for by believing it you yourself will hold a grudge against your brother. In this way you will become responsible for the sin of the one who speaks the evil.
Similar, but not quite the same. But still interesting as it tries to explain how the listener falls under guilt of the speaker. Blogged here for posterity so I can find it again when I look into it next.