Pardon me, but how does this show that Islam itself is not the problem?
It merely shows that being Muslim doesn't save you from Muslim fanatics.
Now, examples that you have mentioned, pardon my cynicism, were more of a collateral damage. The terrorists weren't after these people because they were Muslims. However there have been dozens if not thousands of Shia Muslims vs Sunni Muslims terrorist attacks in Iraq.
Problems with Islam:
1) Apostasy in a crime punishable with the death penalty
2) To qualify as apostasy, one doesn't even to renounce Islam or join another religion, just questioning "fundamental tenet or creed" of Islam is enough. (e.g. Sharia law)
In 23 (!!!) (as you'd guess, Muslim) countries apostasy is covered through criminal laws (which is a violation of universal human rights) it is THAT bad.