I've worked in PR for the better part of 10 years and I've worked for sticky things like politics where context is everything and you are right, editors love to pull out something that "looks" very dramatic to get attention and the Guardian is notorious for this. However, I think the best thing to do is to fight fire with fire. Whatever media you do you should respond to the serious pieces with blog posts of your own. Clarifying things and making your side of the story known is just as important. I am also a believer in that you shouldn't leave your message in the hands of other people. I would then follow these stories up with awesome videos/blog posts of your own that people can interact with on a variety of platforms. That would allow you to get your message out in your way. That way when you do take that interview there is plenty to talk about. Its all about controlling the message.