I've talked about two different issues with the spine, so i'm not sure which you are talking about.
First is the loss of lordotic curve, IE. a loss in anterior concavity of the lumbar spine, IE. a flattening of the lower back and subsequent posterior rotation of the pelvis to account for the sudden loss in mobility, during the lower portion of a squat.
Second is a lack of mobility in the glenohumeral joint, and/or in the scapula. This can come from a number of issues, including tight muscles and excessive posterior concavity of the thoracic spine, I.E. a "humback" (which may not necessarily be visible to the untrained eye).
Now in the video that ring girl presented, her loss in mobility in the bottom of the squat could arise from either issue, or both together. Even with suitably mobile hips, too much stability in the glunohumeral/scapular region or some structural problem can cause the body to look for its mobility elsewhere, typically the spine (this is most evident when an athlete raises his/her hands over head and as a result, the ribs pop out, indicating a significant portion of the mobility has come from the spine). With the demands of shoulder mobility coming from the spine, hip mobility could subsequently be limited to maintain the overhead posture of the hands.
As such i recommend testing the shoulder and hips seperately, rather than together as in RG's video. If you can maintain the lordotic curve down to a sub 10-inch squat with arms directly over head, you should consider competing in the olympic lifts :) If not, you'd be best served developing mobility and avoiding heavy deep squats and full olympic style lifts for a time.