Those with an interest see any critical comments made in the media as further proof of a hatred of Muslims,they don't need trust or belief in the media to believe that. I assume by "Those with an interest" you mean IS sympathisers.

Do you think British Muslims would travel so far across the world to fight other Muslims if there was nothing about the fight in the mainstream media ?

As an aside, I suspect that there are a lot of followers of Jesus who would get irritated if they were repeatedly all lumped together as 'Christians' despite their different cultures, traditions and doctrines.