Tobias,
thanks for chiming in.
The guidance not to have PM play the SCRUM Master role is based on experience from projects where it did not work. Over time we have fine tuned the mapping of SCUM roles to the traditional ASAP Roles as follows:
SCRUM Master - typically team lead or dedicated role in the project guiding the SCRUM teams in their adoption and use of SCRUM principles. Not formally in charge of the teams as a manager. Clears road blocks and helps team stay on target.
Product Owner - one or multiple people from customer site that define the desired functionality of the solution. Typically business users or people that work with the solution. In some cases this role can be played by IT analysts - especially when business availability is constrained (this introduces some challenges in case IT and business do not collaborate well). Defines the WHAT.
SCRUM team - small group of people working on the individual user stories - implementing, developing, testing, etc the solution. Responsible for estimating the effort and planning the details of how to implement. Defines the HOW.
Project Manager is a separate role from these and if the PM is on the consulting side their role is similar to role of Product Owner - as they need to manage the delivery to contract - scope management and change management being the topics here.
Hope this clarifies.
Jan