I could understand that. But in that case, I think one would have to also claim that they are not true believers, but merely criminals exploiting Islam..
Well, I suppose one could say that.
However, I think it's easy for both sides of the argument to suggest that "somebody is not a Muslim, Christian etc." if they do not behave as they should behave,
..or that somebody IS a Muslim, Christian etc. if they behave in a certain way, and profess they do it "in the name of G-d".
I personally don't think that these type of definitions are reliable.
People often have political agendas, and one man's freedom fighter is another man's terrorist.
War is war. There are moral rules for war, and people from both sides often break them.
One moral rule that is often broken is the involvement of civilians. Desperate people do desperate things.
One doesn't need a religion or scripture to be involved with evil.
One doesn't need a religion or scripture to be a pacifist.
I personally don't get the impression that this is the case, but rather that these people are very much religious and feel that they are doing what they believe "true" Islam or God want.
Quite possibly so.
..but that is not equivalent to "Islam is to blame".
If a powerful Christian nation decides to invade another, and considers G-d on their side, does that mean Christianity is to blame?