Talking to the strange

My day job as a reporter often requires me to deal with irate people.
Sometimes they're upset with me, although not very often.
Usually, they're upset about some perceived injustice done upon them or someone they know. Sometimes the injustice is a real one, other times it's been exaggerated by the caller.
In the latter case, I'm understanding. Who hasn't been in a situation where a problem arises and it seems worse than it actually is.
Every now and then, however, I'm required to deal with someone's rant.
So how do I separate the story from the fact I can't take this person seriously? Or the fact that I find what they're saying offensive?
It's a dilemma I don't have to deal with very often, but it does come up from time to time.
When it does, I suppose the toughest thing to remember is that I'm not engaging this person in a debate or an argument. I'm simply listening, writing down what they're saying and throwing out a question now and then for clarification (and to let them know I'm still listening.)
But when it comes time to write a story based on such an interview, it becomes difficult. It's like separating the wheat from the chaff. I have to pick out the ideas that follow the story and put them together into something coherent.
Beyond that, I also have to worry about the possibility of a lawsuit. I mean, I can't just print something because I want to. It has to be true.
So I have to listen to people who tell me someone is conspiring against them, nod politely, and keep thinking to myself that I'll get myself a coffee as a reward for suffering through the insanity.