Actually this is not at all how handicaps and ranks are set up to work.
The definition of rank difference is in stones.
A 2k difference in rank is supposed to mean “these people are evenly matched when the less skilled has 2 stones”.
This would be achieved by having all ranked games played with handicap stones. As I understand it, that’s kind of what happens at IGS, for example: you can’t play automatch without handicap there (as far as I know).
The result of this is that if you are ranked 13k and can’t beat a 15k person witih 2 stones, then you lose, and your rank falls - you aren’t really 13k at all if you can’t beat a 15k person with 2 stones.
At OGS handicap is more the exception than the rule, so that “feels odd” to people who only play here, and our ranks likely diverge from sites where handicap is played more: we “think that” 2 stones is a challenge for 13k vs 15k, as opposed to knowing that it is even because all such games would be played that way.