Anyone who doubts the truth of that statement has a dent in their brainpan.
Compare and contrast the “war on terror”, with WWII. In WWII, whether it be the Pacific theatre, or Europe, establishing a beachhead was a complex, dangerous operation, costing the lives of many servicemen. Meanwhile, Islamists can travel to (still nominally) ‘western’ nations by airliner, or luxury cruise ship. Their advanced deployment, behind enemy (us) lines is then subsidized by the government of the host country, which provides housing, welfare, health care, etc., for as long as required, before activation.