quality management extends beyond the scope of a single project, yet the activities necessary for quality management must be accounted for by each project

they're orthogonal

I would like to answer more generally. You are right in assuming that there are quite a few overlaps, however, in turn that would mean that there are quite a few overlaps between project management and - human resource group - risk group - procurement group - IT group ...

All these groups basically make up sections of a project and all these groups have their own focus within an organization.

I am a Six Sigma Greenbelt and Project Management Professional and I can see where you are coming from but I guess Steven Lowe here put it right: quality management extends beyond a project but any project needs some quality management.

The overlap comes in the utilization of a common framework or processes for achieving a desired outcome in the company.

The quality manager documents and uses processes aimed at consistency and the ability to track how certain types of work on done. The project manager is generally focused on success outcomes of new efforts.

The project manager's work may intersect the quality manager's work when the new effort/project either impacts one of the operations the quality manager has created documentation for or has to function within the framework of one of those operations.

ISO may impact the project manager's work depending on whether the resources used on the project or if the project itself is within the operations certified under ISO.

"It seems to me that quality management is usually the responsibility of one group or person inside a company." This is what is wrong in a lot of companies. Quality is too important to leave to a single person or group. That leads to ticking the boxes, not to quality.

If I read your question right, you're seeing where two Managers might be trying to manage the same work, ie: the Quality Manager overseeing the Project Managers work and both trying to manage Quality?

I would tend to say that this overlap should not exist, IF the project was scoped correctly. Using your example, if the company follows ISO9000 practices, those requirements should be in the project requirements. The Quality Manager, if he is to ultimately be responsible for the product of the project, would have been included as a Stakeholder and should have made sure those processes were included in the Scope documents.

The Project Manager would be responsible for the initial Quality of the project at delivery. The Quality Manager, as a Stakeholder would accept the project and then take responsibility for the ongoing Operational quality of the product.