One part I have a problem with their translation that happens at about 3 mins on the youtube video. - it talks about disbelievers' flesh becoming crispy... like a turkey's. A TURKEY's? - wasn't that a North American bird?
Anyway, if all this video did was show bombs going off and passages from the Quran it'd be one thing. But I don't think you can say that this video is unjustly claiming a connection where none exists, because what it also shows are religious authorities making that connection by citing violent passages, indoctrinating children with them etc.