Different organizations have different structures and different cultures and therefore different needs.
In some cases, you are correct ... the Project Manager isn't. The proper term in this case is scapegoat.
In many cases, you are not correct ... the Project Manager is as much the manager as the resource manager. In some cases, the project manager is, in fact, more the manager than the resource manager.
This latter is quite often the root cause of a dysfunctional team ... the (previous) Project Manager is not recognized by the team as the manager and the resource managers have abrogated their responsibilities for the success of the project. The result is a power vacuum which allows the growth of individual agendas.
Add to this the different structures possible for both the client and the performing team and the situation can become quite complex. Not to mention the third layer which is the expectations of the project manager's management which may have no relationship to the teams' power structure.
Having said that, all managers (operational, strategic or project) need to think of themselves as leaders first. Management is a responsibility of the position.
Project Managers have to have team building as a major strength. (In line with my above comments about presuming a structure, I was going to state that this was because of the need to build a new team for every project. However, I have been project manager on standing teams - where everyone reported to me permanently or to the sponsor permanently and the team members did not change from project to project. Even in this case, there was a need to be a strong team builder.)
Glen Ford, PMP
http://www.TrainingNOW.ca 
