I don't think anyone has ever asserted copyright on the bible. I'm not quite sure what you're talking about? As for pamphlets, copyright can never prevent you from printing something that you created.
In this way, the church had been asserting copyright on the Bible for hundreds of years. It wasn't until the invention of the printing press that they needed a law for it.
It's easy to find legal text today that says it's for one thing but if you're in the know it's clear that its purpose--the side effect without which it wouldn't exist--is unstated or hidden. I'm skeptical that our picture of the 1700's is good enough to solve the same puzzle that far in retrospect, but my hypothesis is that if it was, we'd find things were a bit less about protecting authors economically than a surface-level read would lead us to believe.