Was it ever proven that a mob associated member who wasn't the rat himself actually stated about the bounty? Some guy ratted out the mafia and now to not feel as a miserable fuck he thinks up a story that the mafia has put a large sum of money above his head.

There is no reason to actually kill the rat. While he will live in some Montana 500 people town in the middle of nowhere, he'll also look past his shoulder after every smallest sound, being afraid of getting killed. Years of paranoia will lead him to being mentally disordered and bragging on TV shows like Henry Hill, how he just came to the TV studio escaping a Cadilliac full of mob hitmen with tommy guns chasing after him.

Unless the rat of course comes to the mob himself and they can kill him and get away with it, I doubt there's a hit happening.

Also, the guy already has ratted for example, people already are put in prison. If the rat needs to be killed, then it is the time until the judge gives everyone their prison sentence.