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.
http://www.theguardian.com/technology/2014/aug/30/saviours-universe-four-unlikely-men-save-world
The article is titled "The scientific A-Team saving the world from killer viruses, rogue AI and the paperclip apocalypse", and features interviews with Martin Rees, Huw Price, Jaan Tallinn and Partha Dasgupta. The author takes a rather positive tone about CSER and MIRI's endeavours, and mentions x-risks other than AI (bioengineered pandemic, global warming with human interference, distributed manufacturing).
I find it interesting that the inferential distance for the layman to the concept of paperclipping AI is much reduced by talking about paperclipping America, rather than the entire universe: though the author admits still struggling with the concept. Unusually for an journalist who starts off unfamiliar with these concepts, he writes in a tone that suggests that he takes the ideas seriously, without the sort of "this is very far-fetched and thus I will not lower myself to seriously considering it" countersignalling usually seen with x-risk coverage. There is currently the usual degree of incredulity in the comments section though.
For those unfamiliar with The Guardian, it is a British left-leaning newspaper with a heavy focus on social justice and left-wing political issues.