And the article you link to concludes:
Numerous laboratory studies have shown a direct relationship between bleaching and water temperature stress. Elevated water temperatures have been implicated in the majority of the major bleaching events of the 1980s and 1990s.
Actually that came from your NOAA link. The point is that the "hockey stick" stick pronouncements of coral dieoffs are about as sound as the temperature hockey sticks. It's obvious from even a cursory study of temperature proxies that we have experienced warmer decades and much warmer years in the recent past (500 years). Likewise corals have undoubtedly waxed and waned particularly in local areas over centuries and millenia due primarily to local factors. Ocean temperatures have warmed about 1F over the last century (a continuation of a 500 year trend) but a lot of the warming took place in the arctic.
Before we jump on some corals-are-dying-humans-must-stop-CO2 bandwagon, we need to consider whether there is really any crisis and whether we can actually do anything about it.