I agree somewhat with you and somewhat with the author. IMHO, the control of church over state was more intense before and during the Thirty Years War, particularly in light of the Holy Roman Emperor Ferdinand II's edict in 1619 to force citizens of all states in the empire to adhere to the RCC. While Emperor Ferdinand wasn't the pope (Paul V was pope in 1619), he made sure everybody knew he was Jesuit and believed wholeheartedly in papal supremacy -- to the point of trying to force the Protestant states of the Empire to becoming Catholic. In light of that, the Treaty in 1648 is a step toward separation of church and state (author was right). However, you're right in that more separation was needed after the treaty.
I would associate the development of freedom of religion with the Dutch Republic and its long wars to keep itself free of Spain and other nations. That, and the emergence of the Dutch bourgeoise elite, provided an environment in which freedom of religion could grow, fostered by both Protestant and Jewish philosophers.
Note that the Pilgrims were English expatriate religious refugees living in Holland before sailing the Mayflower to New England.
And the Dutch colony of New Amsterdam was the most tolerant, secular, and mercantile of the colonies. The Puritans of Massachusetts Bay were less so.