You still need insulin to digest protein and for general living throughout the day, even when fasting. It'd be more accurate to say "if you don't eat carbohydrate, you need less insulin, so your insulin requirements may be met by your (degraded) pancreatic output."

On remission: if your Type II diabetes is in the early stages, and is largely due to lifestyle, then a lower carbohydrate diet could help you lose weight and improve insulin sensitivity. If your insulin sensitivity reaches the point where your pancreas' produced insulin is adequate (even for high-carb meals), then you've beaten the disease. This is the remission they speak about.

“...that you cannot produce it.”

It sounds like you are conflating type 1 and type 2. The mechanism of the latter begins with insulin resistance.

>If you don‘t eat carbohydrates, you don‘t need insulin, so it is no disadvantage that you cannot produce it.

That doesn't sound right at all. Protein produces both a blood sugar and an insulin response.

Anecdata and all that, but I have seen quite a few reports of people overcoming their t2 diabetes through low-carb diets.

Whether they were actually cured is harder to say.