The question was, "Why is it so important that MMM be "really" retired? A serious question".
It is neither "important" nor do I care about the "true" definition of retired. I see him as FI, and if he sees himself as FI and retired - I'm fine with that, since he has indeed retired from the rat race since he works only for himself, on projects he enjoys.
If one retires as a lifer from the military, receives a pension, then goes on to a new career or interest, say building or rehabbing homes - wouldn't you call that person retired, even though he or she still works and earns income and is only in their early forties?
Anyway, it's all semantics, IMHO his message is FI - what you do from then on is up to you. In the end, that is really all that matters.