That's like saying the KKK, Westboro Baptist Church, Jehovah's Witnesses, (insert dangerous cult here) aren't "real" Christians. They still believe they are, it doesn't matter what the rest of the world thinks about them, as long as they believe they are doing the right thing.
The problem with Islam is that unlike Christianity they are loosely unified in their belief systems. They in large lines won't call each other out for the hypocrisy or violence. Most Islamists, even the 'moderates' will, if nothing else, quietly avert their eyes when it comes to their interpretation of the Prophet and the Koran. There are some pockets of progressive Islamists that will call out against the violence but they won't go as far as to say that the Koran is incorrect.
Christians have progressed far enough where the progressive Christians will say that the Bible is on occasion incorrect, moderates will say it's allegorical while all but the staunchest of conservatives will say that it's up to God or government to do the punishing. Doesn't mean that the Christian faith is any 'better', it's just slightly better adjusted so as not to upset the majority of people although they still want to take over the world as much as ISIS does (look at how much they have been pushing creationism and anti-science in the last decade)