You can't see your MMR anywhere, so you have no way of really knowing. Those third-party sites are just estimating with their own algorithms. They're okay for following your personal trends over time (am I going up or down), but don't take the number as being accurate at all.
Based on how the system works, there's really no argument to be made though. If your MMR falls low enough compared to the division you're in, you get demoted. There's no other way it happens. You got demoted, therefore you must have dropped too low. You were 4-8 in your last 12 games, so you would have definitely dropped some MMR on that kind of a streak.