A recent PMI meeting had a panel discussion on PMI-based processes and Agile PM processes. What struck me besides the confusion by both parties as to other's position, processes, and understanding was the absence (on both side) of the operative term "Management."
Starting with some dictionary work
Manage - to direct the control or use of
Manage - to succeed in accomplishing or achieving
Manage - to direct or conduct affairs of business
"Projects" are directed, made successful or conducted. But in the end Project Management or Management in general is about "performance." Getting performance out of resources, funding, time, materials, ...
The focus on performance brings into play the management of the aspects of a project that impact performance of those things. Risk, scope, funding, productivity, quality, delivery timing. All attributes that can be "managed" by Project Managers.
Whether through the PMBOK processes or through some form of agile project management - the management of "performance" is the role of the project manager.