Surely part of the issue is that the ice at If you add ice you reduce the equilibrium temp and as a result the < 0C ice temp can be passed to the liquid phase and as a result on to the inner con tain er where you're making the ice cream
the salt dissolving into the water brings the water down to 0... omg time for Farenheit to shine... brings the water down to 0F without freezing it (because of the lower equilibrium temp), which is -17.8C
(Farenheit uses this endothermic salted water temp as its definition of 0, I think because it was the coldest thing Dr. Farenheit knew how to produce in the lab)