It depends on what authority the product manager is given. Most organizations fail to agree on authority vs.responsibility resulting in a culture of confusion.
To eliminate the confusion, I strongly recommend that a product manager draft a DACI or RACI chart as shown for each product. Then visit with each person that is involved with the product and gain agreement as to their role: Decision Maker, Approver, Contributor or Informed for each part of the product market strategy and/or the marketing plan.
Doing so will help reduce future conflicts and speed decision making.