JWs are in constant trouble with the law. The reason given was the refusal of military service not on the grounds of conscientious objection, but because they said they are exempt because they are all ministers. I wonder why they wouldn't use conscientious objection?
Under the draft laws as they existed in the USA in the late 60's and early 70's, conscientious objectors were required to do alternative civilian service, usually at jobs where they could replace workers who would be able to enter combat service. JW's were, of course, forbidden to do such alternative service at the time. Ministers, on the other hand, received a complete deferment. Typically, regular pioneers and "congregation servants" (equivalent of today's CoBoE) could receive ministerial deferments. Other JW's could get CO status at best.