Bullshit.
For one wood and paper have pretty much the same components just paper has a heap bigger surface area. That's why it burns quicker, no were are there similarities with how carbs and fat burn. Fact is fat when eaten has a much better conversion to body fat than carbs converting to body fat.
As for the carb phobia when cutting. I though people have got over that. Carbs can be great for cutting and preserving muscle. Losing weight is about calories anyway. Carbs will give you sustained energy, your body stores them and use them for later, obviously, and unless you have diabetes you won't be getting massive spikes and then a huge drop in energy. Not to mention full liver glycogen from carbs helps minimise muscle catabolism, which is what we want when cutting. Full muscle glycogen will help fuel workouts which will help when cutting and also makes you look bigger.
Now I'm not for high carb diets like in the 90s. But most people on high protein are getting plenty of fat from animal sources anyway. Lowering carbs when cutting pretty much has to be done as to lower calories but carbs aren't the evil of cutting that some people make them out to be and can help.