So when Bro. Martin, our LDS Group Leader (and a civilian), went to meet the Chaplains, there was something of a misunderstanding. They asked for our letters of approval from the LDS church and, as it turns out, we had them. Salt Lake sent us each a letter, addressed to the military, that describes our positions and informs them of our authority to act on behalf of the church. Apparently, the Chaplains never actually read the letters that Bro. Martin gave them, or they would have seen that the letters were informing them that the church had appointed us, not granting the military permission to do so.
The Chaplains were concerned about designating a civilian as the denomination Lay Leader. The Lay Leader program is a military one and appointing a civilian as such in a forward deployed location is unprecedented. The head Chaplain said he'd have to get approval and further guidance from higher up back in the States and that he'd prefer to just appoint the lieutenant as the Lay Leader.
Bro. Martin took him at his word and got kind of nervous about having to call the Stake to tell them that the military had revoked our callings. This was the first I had heard of any of this, so at this point I stepped in and told the Base Chaplain, an officer multiple ranks above me, that he's not the boss of us. Really. I emailed the Chaplains and, speaking kindly but firmly, basically told them that the LDS church does not participate in the military Lay Leader program. I explained that we were called independently of them, that we acted independently of them, and that we were not subject to their oversight.
None of the Chaplains ever emailed either of us back. I hope I didn't burn any bridges there, cause we depend on them for sacrament cups.