Perhaps I'm misunderstanding the second line of your post, so I apologize if that's the case, but the whole idea of the PID namespace is so that the container's

Perhaps I'm misunderstanding the second line of your post, so I apologize if that's the case, but the whole idea of the PID namespace is so that the container's init can run as pid 1 in the container without access to the rest of the host's processes. Likewise for root and user namespaces. (Though I understand that one is really tricky to get right)