No, that not even related. Ko-soto-gake is like uprooting a plant, while ko-soto-gari is like cutting a fistful of grass with a sickle. That's the the auditor means by an 'upward motion', but that is the textbook way of doing it. Hooking with your leg is also considered a form of ko-soto-gake. Gari is a reaping motion, e.g. uke's balance is transferred onto the foot. If the weight is off the foot, and you sweep it, then it is de-ashi-barai.
