I found it at one point and time, but my Search-Fu is apparently weak at the moment.
I have a level 5 Monk (Flowing Monk). Normally, the Flowing Monk does not get Fast Movement (getting Unbalancing Counter instead). I believed that I saw a post indicating that, when you purchase the Braid of a Hundred Masters, if you do not have Fast Movement as a Monk class skill you instead are considered a Monk (0 level), which will give you the necessary +3 Levels for an additional 10 feet of movement.
Hoping that someone official can sign off on it, or someone else who has stronger Google-Fu can link to the original Rules thread question.
Thank you!
(From Scenario #3-13: The Quest For Perfection, Part 3: Defenders of the Nesting Swallow)