In his autobiography “Lieutenant Birnbaum”, Meyer describes going to Rav Hutner zatza”l to get a divinity exemption for the WWII draft since he was scared to go fight in Europe.
Rav Hutner zatza”l told Meyer that since the exemptions were only for full time study, and he was only in yeshiva part time, he (Rav Hutner) couldn’t give Meyer an exemption.
Rav Hutner explained that it would be a massive chillul hashem if the goyim found out that they were going to fight the “jew war” as they called it, while the Jews themselves were fraudulently avoiding the fight.