I can't really speak to the details here - I don't even play go - but I looked at their description of their rating system, and it seems that you've misunderstood the rating system somewhat. In particular, statements like "losing even game to 11k is perfectly fine for 13k, it only means you are 12k or weaker" aren't completely true.
First off, keep in mind that the ? in your rank indicates that the system has little confidence in your rank. As they say:
...the question mark means that the rank estimate (if any) is little more than a wild guess. It may be very, very far from the user's actual rank.
This means that as you play more games and the system learns more, its estimate of your rank could change dramatically.
Further, a loss to a stronger player hurts your rank less than a loss to an equal-ranked or weaker player, but it still hurts. There's even a reference to this in their FAQ:
My friend is 1d and I am 10k. Can we play a rated game?
Yes. As long as you use a handicap of six stones or less. (The large rank difference affects how much your ratings change, but the game is still rated. - - If the stronger player wins, there is almost no change. If the weaker player wins, the effect can be huge.)
"Almost no change" - but not no change at all. And that's with a much larger gap than the games you mention; with a gap of only one or two ranks, the change could be larger.
Finally, a general note: it does make sense to design rating systems like this. If you, say, play a hundred games against a player who's slightly better than you, sure, you should expect to lose more than you win, but you shouldn't expect to lose them all. They do have a math page that goes into more details about this. In particular, they say that their system assumes that if A plays B in an even game, then A's probability of winning is:
1 / ( 1 + e^(k(rankB - rankA)) )
That is, even if your ranks are different, they expect both players to have a chance of winning. So if you're losing every time to people with a rank 1 higher than yours, that means that your rank has been overestimated, and should be reduced. And since the ranking system takes into account every single game, a single loss needs to decrease your rank slightly, which might cause your rank to drop - especially if the system wasn't confident about your rank to begin with.