I think we must understand that Joseph Pilates worked with different people in different ways for specific needs. For instance, it would make complete sense to work with a ballet dancer parallel to balance out that movement discipline which works turned out. Also, it was very evident at the second PMA conference when Lolita San Miguel, Kathy Grant, Ron Fletcher and Mary Bowen spoke about their recollections of Joseph Pilates’ indication on breathing. It was different across the board with each of them.
It is known as well that Mr. Pilates invented different apparatus for different individuals to meet their specific physical needs. There was even a reformer made for the bath tub for rheumatoid arthritis! Mr. Pilates was a genius of the body and invented equipment for various maladies and physical needs.
What I’m getting at is that Joseph Pilates probably did teach Lolita San Miquel the mat work parallel. Working the mat work parallel is not wrong and working in the Pilates Stance "right." In the Peak Pilates education we say work with the standard position of a Pilates Stance but working parallel is fine, too. Work with it yourself and see how this plays out in your body. I am fairly confident that Mr. Pilates also taught his mat work in a slight open stance as well. When you work in this way you do activate pelvic floor muscles that you do not when you work parallel.
One can connect to the low seat and upper inner thighs differently too. However, parallel works wonders for those individuals with wider Q angles, with less muscle and or adipose tissue in their legs and for those who have a tendency to over recruit their lateral rotators. The time has come to analyze movement biomechanically and to understand what works for the individual as opposed to what was “passed” down. In that way we can truly own the work and be authentic teachers.
Good luck with your Pilates practice, Colin.