It is a weird thing.
A lot of people of a LCHF diet find that their liver defattifies.
The key seems to be dropping the carbs low enough.
But there really hasn't been much work on the subject, because all the research bods are still hung up on stuff like 'is LCHF sustainable' and 'will LCHF give you heart disease'.
The people actually living LCHF tend to find it very sustainable, and find that their cholesterol results improve (lowered Trigs and raised HDL) - speaking from experience here - and you only have to read the forum success stories to see how many people are benefitting.
But there just haven't been the widespread studies that prove this. It is as though the LCHF community are decades ahead of the researchers.
And of course, you do always get the people who tried it and failed. But then you get that everywhere - and since I am a failed low-fatter, I completely understand that nothing suits everyone.