I worked at an enterprise software company where our software had to go through "six sigma" quality review process for one of our customers (major corporation).
As you quoted from your friend, six sigma require customer interviews,
task analysis, and understanding processes from the perspective of the customer
not the company. However, from my experience, usability of the software wasn't fully addressed in six sigma until it was too late. Why? I'm sure there are variety of reasons, but I believe companies using "six sigma" often fail to tell the difference between a user and cutomer. For example, our customer (considered one pioneers implementing six sigma process into their enginering practice), did not really address the need of the actual users of the software - instead most of their interviews and task analysis came from upper managment (who really didn't use the software).
Lesson learned: When working with a client using six sigma practice in their organization, interview and indentify both customers and users, although this may not be always be possible.