That's the whole problem with Islamic terrorists, today.
They used the Quran and Jihad as a mean of recruiting Muslims. They interpret whatever they like from the Qur'an and Hadith for their cause, whether it has to do with religion or not. Another problem is that see attack (war) on any Arab is an attack on Islam. They are mixing religion with politics.
Islam can't be blamed for them, but it is hard for non-Muslims to see this, because the terrorists do wave their Qur'an, and do use Islam and Allah as their war-cry or whatever you want to call it. Until they stopped doing this, non-Muslims will always have suspicious on Islam, and this is most unfortunate.
The problem is that these terrorists were involved in abduction and execution of few non-Muslim civilian hostages in front of video, continuing to say that are not only doing to this for Iraq, but for Islam; that's something that we have trouble to forget. But who know how many Muslim Iraqi that they killed in the same way.
There's another problem, where the Muslims don't actively support terrorism, and yet some of their comments would seem to sympathise with their causes, by making excuses or justifications.