I've never really bought into the theory that you can eat too little to lose weight. However, our bodies are extremely adaptable (just look at how different diets are in various countries from first to third world), and I believe that extended periods of very low calorie eating can stall you a bit.
My solution is to vary my calorie intake by almost fasting one day, eating reduced calories most days, and having a splurge day if the scale reads the same weight for too long when I'm trying to lose. Splurge as in maybe 1600-2000 calories, not splurge as in hang at a bakery and sample everything. That 1600-2000 range might be not much of a splurge for a lot of people, but I'm small, not terribly active, and older.
There's a happy medium (for me) between using low cal/fat artificial foods and getting 70% of my calories from fat. I eat foods that are primal. I don't usually add extra fat any more than I would add extra sugar. I trim fat and toss chicken skin (after cooking it), but I don't avoid marbled meats (I used to). When I indulge in a "bullet proof" coffee, I only put 3/4 of a tblsp of butter in instead of the two or three tblsp recommended. IOW, I embrace pretty much everything about primal except the notion (mostly on the forum, not Mark's) that I should toss a hunk of fat/oil/butter on everything I eat. I use added fats judiciously - for example, a teaspoon of butter to fry eggs, not a fake spray (pre-primal), nor two or three tablespoons like when I first started primal.
Anyway, all of that is only what my body has told me. Low carb helps keep me from being hungry all the time. A reduction in calories in a manner I can live with (big supper, not much else throughout the day). And neither shying away from naturally occurring fats, nor superfatting my food. I'm sure it wouldn't work for everyone.
Note: I was a chubby child, so I've learned that whatever "hungry" means to the naturally thin of this world, it isn't something my brain understands. Eating whenever I want has never worked to either lose or maintain for me.
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine