Starving the body of carbs converts the body from a sugar burning metabolism to a fat burning metabolism. When calories get low the body turns to it's body fat for energy instead of glycogen and muscle tissue. Once glycogen is depleted the body converts stored protein (muscle) in to carbs for energy. All low carb diets are fat burning/muscle sparing. The paleo diet is the perfect diet if followed correctly meaning balancing out you acid/alkaline foods and the right Omega 3/Omega 6 ratios. That means eating animals that eat their natural diets. Grass fed/finished cows, deer, wild caught cold water fish, etc. Supermarket bought, even organic beef wouldn't qualify as it is high in omega 6 fats from the grain fed diets.
The paleo diet is probably the most perfect diet but it is also expensive to do 100% correctly. It provides all the amino acids needed for building muscle, naturally burns fat, and keeps insulin levels low. Carbs do not build muscle. Carbs cause an insulin release but insulin also manufactures fat. There are plenty of other hormones that build muscle like HGH (which is low in the presence of insulin, HGH and insulin release seperately and high insulin levels lower HGH levels), testosterone and other androgens.
If you can afford it then the paleo diet is the best diet for anyone, second best options would be Protein Power or Atkins.