If it was something personal and not related to work, then I wouldn't report it because it's none of my business. If it was work related then I would report it, even if the person was a friend.
Depending on what it was, (drug use, etc., that might impact the job), I would probably approach the co-worker (yes, even if they tried to stab me in the back) to let them know that folks are talking. That's the insidious nature of work-place gossip; if the staff is hearing it, then the bosses will hear it sooner or later. If true, then that person can lower their profile by watching their mouths; if it's a lie, they can squash it or refute it.
Good summary, and I agree. Something that affected the job, I would report no matter what relationship I had with the other person.