In what world or frame of reference would doing TDD have "little" bearing on output quality? If you build a system around satisfying some set of requirements it seems logical that output quality would have pretty heavy correlation.
Code that is easy to test tends to be well-structured.
Code that is badly structured tends to be hard to test.
TDD is not a QA methodology, it is a design methodology. It also tends to help quality out a lot, but that's a secondary effect.