One has to have control over the product backlog to be a credible product owner. The primary and critical responsibility of the product owner is to keep the backlog healthy and updated with prioritized requirements. If the product owner has no control then the team will not GET the right direction on what is to be developed. They will not understand the vision and goals of the product. 

Even it will impact the customers very hard, as they will not get what they expect to. No control also MEANS anyone can add or edit the requirements which might or might not be in sync with the customer. The backlog will look like a bunch of random things thrown together. One cannot see the product development strategy behind the Product Backlog Items which gain is a BIG risk to the development. The product backlog is the backbone for any SCRUM team, if it goes out of shape, the team and the customer will not get any output from the EFFORTS they are putting in. The Product Backlog eventually outlines the accomplishment of the product and assists as a master plan for the Scrum Team.