Unfortunately, there is nothing but wishful thinking on which to base that belief.
Mothers speak with pride of their suicidal sons; crowds dance in the streets celebrating the death of the "infidel"; schools teach hatred for the Jews to little children ...
We have yet to hear from peaceful "majority". It seems that any man on the street who is asked about his views spews venom and hatred. I tend to believe that if the "islamists" got out of the neighborhood, they'd leave a ghost town behind.
Don't forget the "suspected collaborators" that we hear about being shot, as though this were a matter of routine. Who are these guys? Footdraggers in the Jihad, one presumes.
Once during the Jenin business When Ashley was posing in the rubble, some gunfire broke out over on the other side of the debris somewhere. "They're shooting collaborators" we were blithely informed. Oh, that's nice, but let's hear more about the Israeli massacre - the important stuff.