sugar and rabbits

"we should all eat less sugars, and prefer fructose to glucose" ..is this true or false?
http://www.medbio.info/
Trying to figure it out I found out this nice website, full of many scientific explanations about the sugar in our alimentation (since obesity comes mainly from sugar excess in the diet, and on the other hand, the brain needs a lot of energy, available easily through sugar, one may be interested to find some equilibrium between mental lucidity and fatness..)

Ok enough introductions.. I will comment here the first article that I read from that website.

SUMMARY:

It deals about what the body does, when no sugar is available. In this case there are only two main energy sources: fat and proteins. The article makes a very interesting observation, which leads to fat as the best substitute:
-proteins are tranbsformable in energy only through the liver
-the reactions needed for that require oxygen
-the liver does recieve most of its oxygen through the portal vein, which has a low concentration of oxygen

based on the above considerations, one can make a quantitative prediction of the energy producable by the liver through protein burning: about 1600 kcal.

What about fat? this can be transformed in energy directly in the cells, no need of the liver for that. Therefore there is no limitation on the energy producable through that process. Easy, isn't it?

Then why did I speak about rabbits in the title? ..that's because of a nice example given there, about this population eating only rabbits.. animals with little fat and a lot of proteins in their meat!! People were eating a lot of rabbits, but still they were hungry! Of course they did not starve (does that confirm the 1600 Kcal estimate?), but that phenomenon was called "rabbit starving".
On the other side, there are other populations eating a lot of fat ("saturated" fat is more energetic, it seems..[this will be discussed elsewhere])..and they had no problems. QED