No, MMR is the ladder of how well you understand the game, it can take into acct warding, TP timing, location, ability effectiveness, damage dealt in each teamfight, ect. It goes a bit deeper than just win or lose.
Grades however are given based on the role you played your champion in, and how well you preformed that role with said champion compared to others in your elo. NOT against all players in general. Its actually extremely easy to abuse the system. If you know what the algorithm looks for.
I disagree with that. I get anywhere from B+ to S (usually) when I supp (what I main - terrible decision in Bronze, I know), but still get SHIT MMR rating. So it's safest just to say NO ONE KNOWS how MMR really works. And Riot's always been okay with that. It's just some biased and arbitrary number that somehow calculates if you are worthy enough to advance.
I totally get what this guy is saying, because it has happened to me SEVERAL TIMES - this season and past - where I'm up for a promo and have been on a great win streak or fast-paced and generally uphill climb only to be saddled with people who DON'T KNOW WTF THEY ARE DOING. It is the MOST AGGRAVATING THING EVER and why I straight up quit Ranked two seasons in a row. They (Riot) obviously have not made any priority or headway into repairing this broken MMR system.