Islam has never kept it's holy texts locked away where only the elite can read or interpret them, a huge part of the religion is an oral reading so everyone can hear it. And there never was a pope-like figure, the Reformation made Christianity more like Islam where either the monarch is the head of the church or the two branches are separate.

This is usually the rhetoric of the "Islam is an inherently evil religion" crowd, who tend to forget just how terrible the Protestants were.