There is the tendency to get defensive about their faith, but that's also a common tactic of the religious apologist, the try to deflect any criticism to any other issue. There's also a tendency from some religious apologists to have quite different rhetoric when speaking in front of a general audience, and when speaking exclusively to members of their own community, and you see them getting uncomfortable when the rhetoric from the latter situation is revealed in the former, as happened with that leaflet. It might turn out to be bullshit, but it wouldn't be the first time that some literature circulating within a Muslim organisation was in dramatic contrast with the public relations image they try to present.
You see it all the time on TV debates. Religious fundamentalists hiding behind the language of the liberal side of politics when defending Islam from criticism. And yet when you actually try to get them to condemn blatantly illiberal actions carried out in the name of Islam, it's like pulling teeth. The best example is The Big Questions regular Raza Nadim, who has struggled to condemn stoning for adultery, and yet is always on TV playing the liberal tune whenever Islam is criticised.