There seems to be little doubt that the bulk of Muslims don't support the more radical forms of terrorism. You are however right that this is to a large extent in spite of some of the teachings of the Koran.
But many religions have had intolerent phases - the early history of the Jews, the Christian Inquisition, etc - but as their understanding has grown they have as St. Paul put it, "put aside childish things." This has not yet happened with Islam; perhaps it never will. I'm not convinced that it's an inevitable consequence of the religion, but I am convinced that its origins were a form of Christian heresy (I perhaps should say, Apostasy). They tend to concentrate on the Christian doctrine of the deity of Christ to distinguish themselves from "the polytheists," but in fact there have been other Christian cults and heresies that denied it as well ... but they have abandoned some even more fundamental doctrines, that is, His teachings. Even if He was just a prophet -- the greatest prophet, in fact -- and not God, to ignore the core of His teachings nullifies any claims to be following Him. Likewise with many of the old Jewish teachings, because Jesus' teachings were very much in line with much of Jewish thought.
However all of this is irrelevant to the present situation. Islam as it stands now has, as a whole, clearly borne bitter fruit. Although there are certainly some adherents who truly want to do the right thing, the religion as a whole must be condemned as one of the evil trees that Jesus spoke of in the Sermon on the Mount.
It gives me no pleasure and in fact great pain to say this, but I fear that modern Islam has been inspired from the other direction. Perhaps in fact it is the religion of the Beast spoken of by St. John the Divine who "causeth all, both great and small, to worship him."