Correct, if your BMR lowers drastically due to sustained increased insulin levels, then you're not at a deficit. However, most doctors are not trained to know that this is what is happening. Every BMR calculator will tell you that you are burning X number of calories, but the only way to verify that is with an expensive lab test that is generally reserved for athletes or extremely ill individuals. So instead, the doctor assumes that the patient must be lying about their calorie intake.

There are "symptoms" for a lowered BMR, feeling cold being chief among them as lowering blood circulation is an easy way for the body to slow down. Mental fog is can be another sign as our brain is the most calorically demanding organ in our entire body.

This model of hormonal driven weight loss/gain is fairly new and just now being studied at scale. Hopefully as time passes, doctors will become better educated and can advise their patients on how best to structure their diet to make their bodies work for them instead of against them.

I highly recommend watching some lectures by Dr Jason Fung about the issue in depth. There are a few on YouTube that are 45+ minutes in length and describe the situation more thoroughly. The TL;DW though is this: if insulin levels are high, the body cannot release stored fat. Eating raises insulin. If you eat all the time, your body will always have high insulin levels and cannot release stored fat for energy and thus will look for other ways to equalize the calories in/out equation.

The fastest way to lose weight, is to simply not eat. It sounds so simple and obvious, yet we've lost sight of the plot in our modern world.

You’ll eventually lower your caloric intake on a keto diet the same way most people over consume calories in a carb heavy diet. It’s just a side effect of decreased food cravings and the obstacles inherent to the diet. You get sick of avacado and coconut oil pretty quickly if it’s all you get to eat. Calorie counting is a fiction mostly.

Body can start to decompose your protein tissues even if fat is there. So, eating your functional cells - muscles for example. It can also turn off less important functions like thermoregulation, impulse/mood control, slows the heartbeat, your activity levels, etc.