I'd say that both the normal curriculum and the answer to that question are wrong or at least misleading. Part of the issue is a misunderstanding of terms. The Puritans did emigrate to the US for religious freedom, but not to establish religious pluralism. The Puritans did not like the way the mainstream Church of England operated, both in regards to theology and in regards to the actual running of the church. They were not particularly loved by most of the Church and the leading elements of the state. Because of this, they were not entirely free to practice Christianity the way they thought it should be practiced. Because of this the pilgrims emigrated (eventually) to America. There, they were free to practice their religion as they saw fit. They did not intend, nor did they claim to, to set up a society where one could practice any religion in the way they wanted to. They were looking for their own freedom, not a general freedom in the sense of the First Amendment.

However, the answer to the question isn't entirely accurate either. As I already said, there was not full religious freedom in England. There were religious tests for office for example. This means that they did not exactly go from a land of religious pluralism to a despotic land of their own creation. The religious freedom of England in that period is a rather amorphous concept. There was a lot more freedom than in certain times and places, but there was not really religious pluralism as we understand it.