Fleisig is a very credible researcher which is why I doubt the entire segment you quote came from him. In any case I'll have the paper soon so I'll let you know.
The way the passage you cite is written the only part that I would assume comes from Fleisig is:
Studies show that at the completion of the transition (top of the back swing) the hips are closed to approximately 45 degrees and the shoulders are closed to about 100 degrees (Fleisig, Biomechanics of Golf).
Which is likely from tabular data supplied by Fleisig and would be consistent with Fleisig's main line of study - sports injuries. Note that the quoted Fleisig paper was published in 'Feeling up to Par: Medicine from Tee to Green'.
Lookng at the remainder of the statement:
The best reference point of when the transition stage of the swing begins is when weight shift onto the inside of the right foot (right-handed golfer) is completed and movement back towards the left foot begins.
For some analysis but not for others.
The transition in terms of a time frame is very short and is completed when weight transfer begins to move forward, and the club completes its movement backwards.
'Short' is a characterization. Relative to key events in the swing transition as defined here is not 'short' in my opinion. It also presumes that the club completes is movement 'backwards' when weight transfer 'begins to move forward'. This is not true for pros.
Research states that the transition of the swing is where additional elastic energy is stored within the body.
I have not seen any research that says this. I have seen research that says that 'elastic energy' in muscles (not 'the body') is minimal and dependent on stretching the relevant muscles as well as a limited time for the muscles to act after being stretched.
This is a result of the lower body moving forward and the upper body still coiling backward.
Here he seems to be referring to 'X-Factor stretch'. Note that this statment conflicts with ...is completed when weight transfer begins to move forward, and the club completes its movement backwards.
X-Factor stretch was specifially noted by the people that first documented it as not being observable in the tested amateurs. Also note that the movement forward by the lower body needs to be initiated before the upper body completes the backswing. There is no 'automatic' initiation of the lower body movement because the pro is 'wound up' (implying they reached the end of their backswing before starting the lower body movement).