I don't disagree, but ratting on the person is not the same thing imho as 'going to great lengths to have the person fired'. It sounds now as if simple ratting may not have gotten the person fired and person B had to rev up and work harder at it.
Or, maybe I'm reading more into 'going to great lengths' than there really is? Well, that may very well be true. I don't know how many specific communications/correspondances took place. Even one is bad, but multiple ones would be even worse.
All I'm saying is that even one correspondance can be enough, and it would be unrealistic for the 'tattler' to not realize that.