the assumption that MMR, as a system, makes is that your "skill" will be encoded in your win % over a large number of games. if you're uncomfortable thinking about that metric as "skill," then don't. instead think about it as a measurement of "how much you contribute toward your team winning a game, on average."
in fact, you could make a valid argument that this metric is not skill. for example, let's say someone found a way to win 100% of their games with 5 APM. this player cannot win a 1v1 lane or land a skillshot or move their hero well with 5 APM but, for whatever reason, they win every game (maybe they found an extremely effective way to play jungle lycan). is this player skillful? not by my definition of that word. but they're contributing a huge amount to their team's chance to win every game.
while the above is a contrived example, situations like this do occur, just to a lesser degree. i know of players who raised their mmr by picking lycan jungle and just split pushing all game. some of these players had ~70% win on lycan over hundreds of games. i wouldn't call them skillful, but i would admit that their presence in a game significantly boosted their team's chance to win, which is what mmr measures. a good example of this is "logonbruce@grace," a player on US east who spammed offlane abaddon and omniknight. he found a way to win dota games that required next to no "skill" (how i would define it) and got to 7k mmr using those heroes only.
what are the problems with trying to measure "actual" skill? * first, we have no objectively correct way to define "actual" skill, and any attempt to base mmr on some subjective definition of skill will result in players gaming the system to boost their "actual" skill rating. * second, "actual" skill is not necessarily something that we should care about. take the reverse of the above: imagine a player so incredibly skilled that he has never lost a 1v1 in his life and constantly outplays people. but he has a 0% win for whatever reason. this guy can beat anyone 1v1, so i'd have a hard time saying he isn't skilled, but he's not contributing anything to his team's chance to win. in fact, he's a huge detriment to his team. does it "matter" that he's the greatest 1v1 player of all time? maybe. it's satisfying to crush your lane every game, and I'm sure he takes comfort in that fact, but should he really have a high mmr when he has a 0% win rate because of decisions that he is making? * Keep in mind, i'm not saying "skill doesn't matter," or "skill has nothing to do with how much you contribute to your team's winrate." skill matters more to me than mmr in dota. i'd rather be 6k and "skillful" than 7k and spamming jungle lycan with 5 APM. also, skill obviously does positively correlate with "contribution to your team's chance to win," just not perfectly.
tldr: the only sane way to measure player performance is win rate. whether or not this is the same thing as skill depends on how you define skill, which is up to you.