Question: "Are product managers responsible for discovering valuable products?"
No. Product managers are responsible for uncovering profitable market problems, and then communicating those problems to product development.
Question: "Let me challenge you. Why do we need a precise definition of product management?"
Broad definitions foster wide ranging expectations which are impossible to meet, and do not allow the focus to build a specialized professional skill set.
Question: "Is the product manager ultimately accountable for product decisions?"
No. This is the role of the program manager.
Question: "Product managers at my company still write product requirements documents (PRD). Can a product backlog replace a PRD?"
First, product architects write PRDs, not product managers. PRDs focus on acutely describing the solution to the market problem via product requirements, while the Scrum product backlog is a general repository that can hold anything.
Question: "What is product marketing responsible for?"
According to PMTK, product marketing is responsible for all outbound activities aimed at generating product awareness, differentiation and demand.