Sorry, I meant starvation ketoacidosis, not diabetic ketoacidosis, but I agree that it's irrelevant to the point since you're still consuming calories. That said, there's a great deal of debate over whether long term ketosis is healthy for you; certain native peoples (the Inuit for example) supposedly lived in a state of ketosis, but some were only in ketosis seasonally, trading for seaweed and other plants from other tribes.
Nevertheless, you didn't refute the point that ketosis only occurs with low carbohydrate intake, indicating that carbohydrates are preferentially burnt over protein and fat.
'Complex carbs' just means it takes more effort to digest and extract out of plant matter, you're still eating carbohydrates. That puts a big hole in your supposition that you can live without 'carbs'.
I'm not aware of any other 'complex carbs' other than glycogen in meat.