What service? If somebody washes your windshield without you asking, it isn't a theft of service to not pay them. A theft of service arises from entering into an agreement and then failing to pay as stipulated in that agreement.
Copyright isn't an agreement you can choose whether to participate in. Copyright is a legal enforcement system that imposes legal liability even on those who don't use it. You may not see this legal liability as "harm", but it absolutely is. Arguing that copyright extends to training is arguing for a dramatic increase in the scope and power of this legal enforcement system.