Nope, not just low carb.
Excess protein will be converted to glucose by the liver, whether you're in a ketotic metabolism or not. It has to go somewhere :-)
Fat is mostly just used to make hormones, connective tissue and cell membranes, among other structural components, and stored in adipose tissue. The latter is stimulated by insulin -- i.e. cranked up -- so quite a bit more will be stored when there is plenty of carbs in a meal along with the fat.
TAGgers account for all three every time they eat, no matter what the mix. That's what I'm doing these days -- bolus carb weight 100%, 1/2 protein weight as carb equivalent, and 10% of fat weight as carb equivalent.
I always pre-bolus the carb insulin, wait 20-40 minutes, then start a 4 hour square-wave bolus with the protein and fat insulin when I start eating.
Works really well, and gives me the chance to cut the protein/fat insulin short if my BG's fine and heading south. Bolusing the entire ball of wax in a single impulse doesn't give you this flexibility.
Of course, this is only possible with a pump. Can be done without a CGM, but it's a lot more work.