Yeah, thinking is one thing - necessarily disclosing in surveys what one thinks quite another. It should be clear to most people. But of course if they really want to believe something no matter what, they´ll first of all get rid of any such obstacles as reasoning and logic.
Also, we don't know their terminology and methodology. Leftists groups such as Pew are famous for twisting their survey methodology, to justify their political goals. Also, they might have surveyed only the urban regions, where the population is more liberal and educated. Strongholds of Islamist insurgencies are not always accessible for these survey groups.