Tobias,
you got it. With one exception - we do not only manage development this way, but also configuration and other work in the project.
Secondly you are referencing Project Manager (company) - if you mean PM from integrator then it is correct. In internal projects there may be less formal way of managing scope. The PM as Product Owner is a concept you need to put in place in contractual situations where PM is responsible for delivering the solution specified in the contract - she is then the Product Owner controlling what gets in the backlog and what stays out.
Have a great weekend,
Jan