Ranks actually do mean nothing

Any player has with probability 1 of reaching the top rank just by playing enough games.

Assumptions -

1. This player has a non-0 chance of winning any game
2. This player's actual skill level is not negative infinity
3. The number of games needed to beat the top rank is finite
4. This player has >50% chance of winning whenever his elo drops below his actual skill level.

Let p denote lowest possible probability this player has of winning a game. p is not 0 by definition. Let N denote the number of games needed to surpass the top rank. His probability of getting there in a single attempt is p1p2p3*...pN>p^N>0. If he fails, he can try again. If his rank drops below his actual skill level, by random walk theorem, with probability 1 he will return to his actual rank and can try again. With probability 0 his elo will drop to negative infinity. lim1-(1-p^N)^n has n goes to infinite is 1.

Therefore with probability 1, this player will reach the top rank.