I think there's no real basis for the contention that the term "quality assurance" was devised to signify a more sophisticated approach to quality control. American business has a marked propensity for believing that changing the name of something changes the essence of it. Personnel departments became Human Resources, Data Processing departments became Information Technology, Accounting became Finance, etc., etc. It's only fitting and fair that QC should get a new name too.
In one place where I worked, where managers truly believed in the magic of renaming, buyers became Supply Chain Analysts. Nothing changed about the work they were doing and nothing was improved. My theory is that upper level managers somehow feel more important when they have a lot of analysts working for them, instead of plain old buyers.
Some such manager somewhere in the past decided that his QC department would be much more effective if it were given a new name, and Quality Assurance was born. A bifurcation has occurred with differentiation between QA and QC as a matter of back-formation rather than the distinction being a part of the original idea.
Everyone is, or should be, working to control quality, and when quality is controlled, quality is assured.