As has been previously mentioned, someone with type 1 (I am more than my diabetes so refused to be called “a T1” and offer the same level of respect to someone with type 2), does not take zero insulin: they will still need basal insulin. Exercise, etc can lead to hypos without carbs due to the reduction in basal needs. For example, with an insulin pump, I suspend my basal when exercising to avoid hypos but when injecting, this is not possible.
And don’t forget that bolus insulin is needed for protein when someone with type 1 eats a low carb meal. Another reason why it is difficult for someone with type 1 diabetes to have no “exogenous insulin”.