In my closer examination and slow playing the video, there is a slight transition of movements from acknowledging the successful putt, pausing-shows balance, and going into picking up the mini which results in moving forward because while picking up the mini, the shift of weight goes forward from picking up the mini, not a continous movement of the putt itself.
The act of picking up a mini before moving forward, i would consider control of balance. I just tested this out on my basket with mini and putter. I was not able to successfully make a falling putt and pick up my mini most of the time, when I was able to get my mini while making a falling putt, it was obvious and looked desperate.
When imitating the exact movement and stance as Barsby, I felt in full control of my stance and felt the exact shift in movements while picking up the mini that leads me to lean forward, seperate from the putting movement. Trust me, test it out, you will feel in control of your balance if you imitate the video. Its the reaching down really low that pushes you foward, you can easily lean foward without reaching down and come back up easily on flat grond... PROVE ME WRONG...
As for the attire that Barsby wears, I love the guy, but yes, I encourage TD's to enforce the attire guidelines.