Well...are stereotypes really the only reason for that? Does the Koran, and the relationship of Islam to the Koran, have nothing to do with it? Couldn't it be that at least some people wonder if Muslim liberals still have the Koran to contend with, just as Christian liberals have the Bible, and if there is some tension? Couldn't some people think that liberalism is just more difficult for Muslims for a lot of reasons (family pressure, customs, the Koran, friends, and so on) and that different people can mean different things by 'liberal'? I would say it could, and that people who are slow to be convinced are not necessarily simply heeding stereotypes of the violent Muslim. They might be, but they might not.
In other words: Are stereotypes really the only reason? Couldn't it just be (insert a whole long list of stereotypes here)? Of course, technically she's right: it might not be the stereotype of the violent Muslim; it could be some other ill-founded and illiberal stereotype.