I very much liked this question. Spent more than an hour thinking about what the optimser must be doing. Once it clicked it was obvious, but it's a problem I'd never thought about before.
I will certainly be careful in future to look and see if I need to have filtered statistics in cases where the flat distribution assumption will cause misestimation that could lead to problem. I guess the reaon I never thought about it before was that it had never caused performance issues that were as important as other performance issues (many of them not SQL).
Thanks very much for the question.