Obviously you see it as different training methods. I don't agree on that. To me they are faculties of the mind, not trainings. When you focus on the breath, both samadhi and vipassana are needed and trained. As may be obvious from experience, you can't have a still and sharp mind without knowing how to do so, so samadhi requires vipassana. On the other hand, you can't have true insights without a sharp mindful mind. A dull mind just won't see the way things are, so vipassana also requires samadhi. So, the two are supporting each other and are not separate.
That's a very interesting point you make: Samadhi is contingent on sati and sati is contigent upon samadhi. You can't really have one without the other. When we are trying to develop a deep samadhi, we must exercise sati as well. In the cultivation of samadhi, sati is used to let us know when we've wondered off from the object of focus. Likewise, when we are cultivating sati (which I assume is the essence of Vipassana), we need samadhi to focus our mental resources on the Vipassana practice. Thus, to cultivate one is to cultivate the other. I see that, but at the same time, samadhi development is clearly indicated as a separate practice my many of the major teachers. S. N. Goenka, for instance, has his students practice Anapanasati for the first three days of his ten-day retreats and thinks of it as a unique, distinct practice wholly apart from Vipassana, which only begins on day 4. He states firmly that all the Anapanasati in the world will not promote insight into anicca, anatta, and dukkha--that Vipassana is needed for that. According to Goenka, Anapanasati is only good for developing concentration, which can then be applied to Vipassana (which for him is body sweeping). Shinzen Young also regards Anapanasati as a concentration building exercise, and little more. It seems clear that there are ways to integrate Vipassana into Anapanasati, some of which I've discovered in this thread, but many notable teachers regard them as separate, even unrelated.
"Concentration practices are insufficient for realizing insight into impermanence, even with the concomitant undercurrent of mindfulness." That is the assumption I have been working under, being the view transmitted to me by the aforementioned teachers, if I understand them accurately. If anyone disagrees with that quite fundamental assumption, I'd love to hear their case. I think it would be just great if concentration practices could lead to meaningful, permanent insight, as they are relatively straightforward to understand, practice, and teach. I just thought it didn't work that way.
Thanks again to all for the helpful discussion.