Hope i cleared that up.
If you wins against 1800 several times in a row until you reach 2000 then you are playing like 2000. Rating is about probablility and expectation. If I remember correctly 200 difference means that stronger player is expected to get 75% of points and weaker - 25%. If that's your result - this is your level.
Rating almost means nothing. I can play some players in one town at say 1800 rank and clean their house and then go the opposite part of the country and get destroyed.
If you want to be a true 2000 rated player than you have to play and think like them.
Play and think like who??? Like 2000 from some town or 2000 from other side of the country or 2000 from some internet site??? Ratings mean nothings when comparing between different pools of players, but they mean a lot within the same pool.
Yeah, so if you beat someone 200 point lower 3 out of 4 games over and over your rating wont change... The problem woudln't be playing many different players 200 points below you, the problem would be beating the same person 10, 20, etc games in a row if their style is easy for you or they're having an off day. That's when online ratings can get skewed.
I know one site that is very easy to do. Once 5 players did it then almost every broke it as the first 5 showed how. We play 50 games a day easy. It was too easy. After a while the 1300 rated players figured all they had to do was play quanity games over quality. Have to add the rating system was off....way off.
Playing the same player issue. Those players were different from chess.com. They did not care if they lost 5-10 straight games. Why? If they wait long enough they can get the points lost be beating somebody else. They might even challenge you. Why? They use what you did to them on somebody else.