A pirated book likely came from a purchased original.
Imagine a pirating service which ensures that a given file is only being consumed by one machine at a time. So if I want to watch the newest blockbuster, I have to wait my turn, and once watched, I cannot watch it again (without getting in line). In effect, the movie is checked out a single instance at a time, just like how a library checks out a single book at a time.
IANAL but I'm honestly not even certain that the piracy service you describe would actually be illegal, or at least that it couldn't be done legally.