Yeah, but with this new study out about how the Arctic Ocean was once so warm, you really have to wonder how the corals got by in the warm world of that time. Are the mechanisms just unavailable now? Was it only very specific corals that made it through that heat and all the subsequent diversity since then? If the diversity was there then, why are the corals having such problems with warming now? Interesting stuff and I think all of the qualifications are just because they hadn't expected these results and no one knows the answers. Cool time for science, at least.
It is possible that at any time when there's a shift most of the corals die out. The survivors (with the rare beneficial variants) then expand to fill the vacated niches. It's a natural process over the long term. When a reef in the tropics dies because it's too hot, a reef forms in temperate zones where it's cooler.
Theoretically the whole population of corals could die out because they've lost their original diversity through genetic drift (and symbiosis is in some ways more complicated than genetics), but since that hasn't happened through all the past extinction events I don't think it's likely now.