With respect to fruit and other items in your link the answer is "no", the more active rabbit is not likely to be consuming a significantly larger proportion of hay to make it correspond to that of a rabbit with a larger body size. Moreover, the rabbit's intestinal track is the same diameter of other buns his size, and thus a larger sugar intake could create a disruptive pocket of undesirable flora around the sugar bolus.
Sugar can destabilizing a rabbits GI flora, which for a rabbit, can be deadly. As such, before trying to add the extra sugar to the buns diet, you might want to ask: "Is really worth risking your rabbits health just to get her to beg for an extra half of cherry?"
Further, there is a gowning number of scientific studies that seem to indicate sugar is actually toxic to all animals, and that sugar addiction is real and can be on par with that of cocaine. While this explains why your rabbit tries to crawl into your mouth to find the rest of that banana you ate, it should also leave you concerned. Thus, erring on the low side of sugar intake is the best choice for a concerned owner.
With that said, the single teaspoon of sugary foods per 2 lbs of rabbit is only a guideline, and not all fruit is equal. Papaya, for instance, contains enzymes that help your bun digest, so a little extra isn't bad (but the less sugary tablets are preferred). Further, the difference in sugar content from an just edible banana, to an almost over ripe one can be close to double. Thus, you bun might be fine with some variation.
Occasionally, I feed up to 2 teaspoons of just barley ripe banana to my 2 pounder and haven't had any issues. However, as the banana ripens, leaves behind string like pieces that I use in-place of breaking off a chunks as the strings provide prolonged interaction and extra opportunities to teach your bun new tricks.
Yet beware, overweight buns, and buns with GI problems tend to consume less hay than their more fit counterparts, and therefore should exclude sugary foods that could irritate their GI track and increase their overall caloric intake.
Aside from fruits and sugary vegetables, pellet food is another way rabbits obtain sugars in their diet. The sugar in pellet food, is more dispersed and thus much less likely to cause GI floral issues. Because of this, and the larger portion that pellets take up in a rabbit's diet, you might consider slightly increasing pellet intake for extremely active buns.
The HRS recommends no more than a 1/4 cup per 3 lbs of rabbit. This recommendation is for normal activity levels and assumes the weight of the rabbit correlates with the number of calories required to sustain it and thus it's overall hay intake.
Smaller rabbits, such as dwarfs are generally more active than normal and large rabbits, but tend to maintain the overall hay intake to weight ratio. This is because, the bigger they get, the more energy they need to move. Thus, it's not advisable to correlate high activity in smaller buns to higher caloric need.
However, if you happen to have a large rabbit that is highly active, he will increase his hay intake in-order to make up for lost calories. This increase in the amount of hay he's consuming means that your might also proportionally increase his pellet intake.