Many studies measure total calories as well as sugar. The study linked above explains the correlation between the two. High sugar provides little satiety, leading to higher total caloric intake because you tend to eat the sugar in addition the other, satiating calorie sources.

You do not simply control for an additional variable when you know there is a direct link between the two. You study it as a dependent variable.

Edit: replaced "fulfillment" with "satiation". Sorry about the vagueness, I thought the meaning was pretty clear from the context.

Which is a reason why you have to control total calories to know that sugar consumption is actually a detriment to health (and at what quantities) and not just a caloric surplus.

"fulfilment" is a vague term and you're veering off the topic into a strawman argument

Yes, and here is the thing: you can't control for the total calories and vary only sugar intake. The change in sugar has to be offset by something else to keep the calories constant. So then to know whether a sugar change is responsible, we have to try different experiments with the same delta in sugar, but varying compensating substitutions.

I think you're missing the point.

It wouldn't make much sense to keep the groups isocaloric but replace the calories from sugar in one group with say, protein in another. You wouldn't be measuring the same thing any more.

The entire point of the study is comparing monosaccharides to polysaccharides and observing changes in 'health' (excuse the vague terminology). Sugar is substituted with a longer chain carbohydrate in well planned research.