It depends on each situation. If it is a good friend who is "supposedly backstabbing" me, I would delve further by asking HER directly. But if its acquaintances or people I barely know, I shrug it off. I know that there are a few Aders who gossip about me but I don't care as it is not worth my time/energy to confront them. Let them remain pathetic.
When it comes to news, I always do research but I usually go by my personal experiences when it comes to actually believing in it or not, rather than go by what others say.