They are only claiming they are. It doesn't make Islam is doing. They are some intelligent psychos who have some political gains in mind. If Islam is telling them, then twister's statement can be true, but it isn't and hence, it is wrong. So please don't spread misconceptions.
In the media ISIS is portrayed (and accepted by the public opinion) as the voice of radical islam. Across the islamic world tons of ppl supporting them and agrees or partially agrees with their views. IN the meantime apart from some theatrical moaning the moderates are silent. Sorry to say but in this days they are the "public face" of islam.
I understand what you are saying and I do believe media is the problem. As far as I have seen, US* medias are more active in making Islam bad. Most people who support them are going for political gains and most of them are non-Muslims. Anyway, I think, I alone can't do anything when widely influenced medias spread lies.
* I am not an anti-US. See wiki.