The 15 games thing only works if the entire rest of the playerbase is established at their ranks. Also, that came at a time where you had much higher winstreak bonuses (but also much higher loss-streak penalties).
Going from Season 1 to Season 2 (where the SR scale went from SR 1-100 to SR 1-5000), there was somewhat of a reset. Pretty much the entire playerbase was compressed into the middle again but not fully like in Season 1. And games were very, very unbalanced and it took nearly the entirety of Season 2 (which was a 3 month season still at that time) for proper sorting to happen again.
The statement about SR and MMR being linked is here:
Pretty much everything Blizzard has ever said about Competitive matchmaking is compiled into the References section of this topic: