Let me address that. I actually know Anna very well. We were graduate students together back in the 1980s.
If you look at the assessments as to what will happen to corals, there are two effects. One is bleaching through temperature and the other is through their inability to grow because of ocean acidity.
The amount of carbon dioxide we're putting into the atmosphere is such that the acidity levels of the ocean towards the middle of the next century will reach levels that have not been reached in 300 million years of earth's history. This spells the demise—and there's not much we can do about it, unless we act now—of all the world's coral systems.
I suspect that when you see statements such as you just heard there, they are not alarmist; these are very real statements, and you haven't seen anything yet.
Look at the barrier reef. This is an ecosystem that's destined to death, and I don't think there's much we can do about stopping the death of the barrier reef because of the warming and the acidity we have in store due to emissions that have already happened.