I don't think you absolutely need to ask permission but I found it very helpful to be in contact with people from the platform (my course was provided through the Australian provider Open2Study) and the lecturer of the MOOC. I found they were very interested in the Learning Circles model and keen to receive feedback about the success of the course. I'm not sure about the "big 3" but I developed very productive relationships through communicating with the providers.
In the course I facilitated, not all participants signed up (2 were happy to just attend with their partners). However, those who signed up felt committed and were very pleased to receive their Certificate of Achievement at the completion of the course.
Good luck with your Learning Circle!