For what it's worth, this mostly doesn't actually happen. There is some good science behind maintaining ketosis in children under careful monitoring by a physician. Most of the empirical evidence in adults is that it's hard to achieve and harder to maintain. The weight loss some people achieve on "keto" diets is mostly just due to caloric restriction when it's been measured carefully.
The upside is you don't really want to have your body in ketosis anyway.
I've ketoed before for weight loss (and am starting again soon) and when I was quite strict with it I'd be well into the ketosis range on those pee strips.
If it's not a sign the body's in ketosis, what is it a sign of?
Also, fwiw, I lose significant weight on keto without moderating my calorie intake at all; fatty meats, cheeses, butter, oil, etc., plus a lot of vegetables. If it's not ketosis, what is it?
Unless you were very carefully tracking calorie intake before and on the keto diet, it is not justifiable to assume same caloric intake, even if keto food seems very calorie rich.
Of course you're right, in the other sense, that if you don't eat any carbs your body will be burning the fat you ingest instead, and that this will show up in your bloodstream. You also won't burn any weight this way unless you have a calorie deficit (as you note, it's "temporary").
Note that when OP said that "it doesn't happen", they didn't mean ketosis doesn't happen. They meant that meat-heavy diets don't result in weight loss because of ketosis.
But the basic idea is simple and works.