As a retired military chaplain (Army), that simply isn't the case. Protestant chaplains are not permitted to conduct Catholic services, and Catholic chaplains cannot conduct Protestant services. A Methodist cannot do a baptist service, and etc.
Non-denominational in the military is never Catholic and is really just a heinz variety of protestant.
Perhaps the Army is different than the AF, but in no case should denominational services be led by any chaplain not a part of that denomination.
It has been my experience that Army chaplains hold seperate denominational, and non-denominational services. Keeping the two seperate. One being specific. The other being generic. I must add, that while I agree with the position, should they make a move, by order, to enforce. Rebellion would then be my choice.