If I change the airplane to use a chrome shader, now I need two bounces. There are places where the water reflects the plane which reflects the sky (two bounces in one chain) and there are places where part of the plane reflects another part of the plane which reflects the sky (two bounces). In these places, since I rendered with one bounce, the contribution from the second bounce is missing. That means the water reflects a black airplane, and the airplane reflects a black airplane.
Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)