Water isn't toxic, yet drinking too much water can cause your blood to become so diluted that you can die (water intoxication/hyponatremia). And yet water is essential for life.
Consuming sugar (in some form, not necessarily sucrose) is also essential for life. It's what your brain runs on. So to call it toxic is quite a stretch.
I'm not criticizing the research. I haven't read the paper and I probably won't - it's not my field. But I am criticizing the overly broad generalities in the NYT article.
Consuming any amount of any form of pure sugar will spike your blood glucose. If it's a small enough amount, the spike will be small enough that it won't do you harm, but the human body evolved to handle gradual rises in blood glucose, like complex carbohydrates cause, not spikes. Comparing that to water is a stretch.
By the logic you've laid out, cigarettes aren't toxic. Smoking them can cause a variety of diseases that kill you.