['So I accidentally got someone fired for something at work.', "That sounds bad. I know it wasn't intentional but what happened?", "The person bragged about doing something, that they didn't actually do. Which was highly inappropriate for the job we had. I had to tell the manager due to liability issues. All for it to not even be true."]
Well you did what you were supposed to do. It's their fault for saying what they said.
Someone told me something at work that was inappropriate of them. I went behind them and told the manager what was said as I was concerned . Turns out the person was lying about even doing it and was fired for it.