"Minutemen were a small hand-picked elite force which were required to be highly mobile and able to assemble quickly."
I think we're being enamored of the term "elite" here.
"By the time of the Revolution, Minutemen had been a well-trained force for six generations in the Massachusetts Bay Colony."
Nevermind that militia generally had been around for generations in Europe. Long existence doesn't make good military.
Regardless of the history here, it must all be taken as RELATIVE terminology. Minutemen were PART of the militia, and their main purpose was to be ready as quickly as possible, to meet up the enemy in the local area as fast as possible. Notice for all the description, you aren't told what "well-trained" means. Neither is it clear if all are provided w/uniform weaponry, or whatever. And I think you'll find there was nothing beyond local "control" of minutemen - like the militia of which they were part. It's not as if we had military experts roaming the entire countryside who knew just how to train and maneuvers, etc. Washington was all too aware of that - and that's w/the "standing" army! He himself had to look mainly to Euro's in the army for help in getting military knowledge and discipline and disseminating it. The rest was guesswork, FAI!
They may have been better than plain militia, but that's not saying much! Trust me, these guys were NOT the equivalent of British regulars!
They elected their own officers & non-coms . . . not that it mattered much, for they didn't even follow their officers' orders if they didn't want to. At Lexington and Concord, most engagements didn't even take place in company strength---they were "run and gun" battles along the road from Concord to Boston.
About the only good thing you could say for the militia as a fighting force is that a large number of them were veterans of the French and Indian War.