Hi Nicksu, this is simply not true.
You need essential fatty acids EFA but that's not the same as fat. 
You also need to take into account where you're at in a diet if it's at the end, where you have lost a lot of body fat then you need something, either more carbs, more fat or more protein, to supply you with energy.
But at the beginning of a diet like
@engie1967 where you want your body to
burn its own fat for fuel its not the same thing.
Fat can be a good choice as it has the
duel function of not increasing bg levels and can be burned for fuel almost as efficiently as carbs.
A Low Fat diet still contains butter, cream and cheese dairy fat, just less of it. It mostly wants you to cut out animal fats.
This idea is very logical 
if you don't give your body
carbs or fat it
needs to find the fuel to run from somewhere else and there's only one place to look the body's own stores of fuel Fat or Protein (muscle)
But LCLF is high in protein which takes longer to convert to fuel and should be sent to the muscles to promote repair and growth through exercise, which mean it should
tip the balance in the body to burn Fat.
But like everything it's how it works for you @bulkbiker was probably closest with LCLF can up your carb intake and some people are less carb tolerant than others
if it raise you bg then it's a bad choice for you.

But it's still LC it's in the name.