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. 
I agree, but still feels bad to get someone fired at times.