BTW, those pictures are worthless for daily temp fluctuations. If you read the article, though, there is a little more info.
Personally I find it a bit weak. Most of the daily fluctuation data was taken at a single point, in a single month, in a single location. And even then, most of the days had only about a 1.5 degree Celsius change (although a couple days had bigger changes). I think its quite a jump to go from the corals can tolerate an occasional big swing to its no problem at all.
I don't think there's a convincing argument either way personally.
My personal experience is that temp swings were a bigger deal for the fish than the corals. Big temp swings seemed to lead to ich outbreaks in my early tanks. However (and its a big however), this is before I was very experienced. I didn't q-tank, my husbandry habits were subpar (although not awful), etc.. So I am hesitant to draw a lot of lessons from it. This does seem to match up with other people's experiences though.
IMO, with no convincing evidence either way and lots of anecdotal "evidence" that swings are bad, I take the conservative approach and try to keep things stable.