Whatever you are referring to Losingme, it's pseudoscience.
You are over complicating and placing unrealistic significance on what is basic GCSC science.
The Basal Metabolic Rate is primarily affected by the portion of fat to muscle in the body and the amount of exercise done.
Other factors include age, body size, sex, genetics, temperature and health/illness.
Eating 100% protein will not change your metabolism and will not lead to weight loss unless there is a calorie deficit. The calorie deficit is what causes weight loss, not the protein content.
Eating 50% protein will not change your metabolism and will not lead to weight loss unless there is a calorie deficit...
Eating 30% / 25% / 20% protein will not change your metabolism... You get the idea.
(although for the sake of completion I should say that having zero or exceptionally low protein levels from a very restricted diet, the same as having zero levels of any other nutrients, will cause malnutrition.)
You seem to be confusing matters with the fact that protein intake does accelerate muscle growth. It's why body builders and athletes take protein powder, to build extra muscle. This is true. It does not follow that not having high protein intake causes muscle wastage. It doesn't. It just means muscles can't get bigger when you work out. It doesnt mean muscles get smaller without the high protein, just that they wont grow as fast. If you're not working out anyway, then muscle building is irrelevant.
Protein levels themselves do not affect weight loss. Calorie deficit affects weight loss. Only calorie deficit.
A high protein diet is good. Fat and carb levels will be a more individual thing but ensuring that a high proportion of your daily calories are protein is definitely a good thing for your health. It does not affect muscle wastage though. Not exercising causes muscle wastage.