OK I may or may not be correct but the only time I remember the "200" ranked rounds being mentioned as I rose through the tiers was when Champion Tier was first introduced. IF you were a Tour Legend at that time you could play an additional 200 ranked rounds to become Champion with the appropriate average as well. As far as TC I believe it is 500 ranked rounds and an average of 55.0 or below based on TC's I know that turned TC the first round they played (The morning we got Wolf Creek) and then their average shot up based on the first round they played as TC.
Just one mans opinion but I am a Champion with a 56.84 average with well over 500 ranked rounds as a Champ and I know other Champs in the same situation but with 55.XX averages and over 500 ranked as well that have not tiered up either so 55.0 has to be the number in my mind.