Which is what I said from the beginning. If he were to admit in a civilian legal proceeding, it could be used against him in a military proceeding. it makes perfect sense, from his standpoint, to use the 5th. it protects him from the UCMJ, and possibly anything in the VA court. If he did lie, then you also have the issue of a false statement, perjury, which would be a totally different offense, and he could be prosecuted for that. They may actually have done nothing about the adultery in the AF, but if they have a statement from him, and he nows says something different in VA. new charges are possible.
Not saying it is right, or fair, but it is understandable, as to why he would do that.