I think you might have missed my parenthetical! :)

Most skill ranking systems actually don’t show the rating they use for matchmaking. There is usually a separate level that is shown rather than what is used for matchmaking.

This is because many people get really upset when their displayed rating doesn’t go up after playing a lot of games, but with a skill level that is the expected result when you finally reach your true skill rating. Players won’t constant progression, so they will show a separate score that keeps going up while they use a hidden true rating for matchmaking.