In all the discussions, it is clear that very strong opinions exist. Some are born of tradition, others are born of convenience, and still others are born of lack of clarity and understanding. In any discussion, especially of a topic as subjective as "quality", it is important to be clear on the definitions as a basis for that discussion. Having done that, "sticking to your guns", as some of the eminent contributors on the LinkedIn discussion have done, is unquestionably a valuable project trait for a project manager. But just make sure you are sticking to the right guns!
However, to answer the original question: "'Quality' first or 'Project Management' first?" in the sense of which discipline came first, the answer is most likely "corporate quality management". In the sense of which discipline is highest in the pecking order, again the answer is "corporate quality management" since it is somewhere near the top rung of the ladder. However, in the sense of which discipline should be tackled first in the life span of a project, the answer is equally clearly "project management". That's because, like scope, cost, and time, quality management is a subset of project management.
Nevertheless, at the end of the day, interest in quality, in all its forms, outlasts all the others by determining the potential duration of the life of the product.
R. Max Wideman