In a way, your Scrum Master is correct that Product Owner is the boss of the Scrum Team. Many organizations have matrix structure where employees have one direct boss (responsible for employee's performance evaluation and other management tasks) and an indirect boss (to whom an employee reports for a temporary duration). When you think in those terms a Product Owner can be termed as a boss of the whole team (not the boss of an individual).
From another perspective, for the scrum team a product owner is the customer (or customer's representative). PO is responsible to manage requirements, to prioritize them, and to accept/reject functionality delivered by the scrum team. In effect, PO has some of the powers which traditional bosses used to have.
Let's recap some of the responsibilities of a Product Owner (Scrum Reference Card
by Michael James):
- Single person responsible for maximizing the return on investment (ROI) of the development effort
- Final arbiter of requirements questions
- Accepts or rejects each product increment
- Decides whether to ship
- Decides whether to continue development
Product Owner has the power to say "no" on what goes into the product backlog and when stories go into a sprint backlog. As Steve Jobs said: "Innovation is not about saying yes to everything. It's about saying no to all but the most crucial features."
From the above list, I would say that a Product Owner has some critical responsibilities and appropriately has equally critical authority and decision powers (so he can be assumed to be the boss).
However, the Product Owner does not assign/distribute tasks within the scrum team. PO does not estimate stories and a PO does not tell you how a particular task should be done in terms of technology.
A related note:
A Product Owner does not have to be a senior designation/person like an architect or development manager (or any kind of manager). PO's role can be assigned to any person who carries clear vision of what is being developed and why. PO should have great communication skills to convey that vision to the scrum team. Should have quick decision making skills. Should have updated market research information. Should be able to foster collaboration.
Product Owner On One Page:
As the name suggests, a product owner should own the product on behalf
of the company. You can think of the product owner as the individual
who champions the product, who facilitates the product decisions, and
who has the final say about the product, for instance, if and how
feedback is actioned, or when which features are released.