It turns out, according to a number of reports, he received a BCD, not a dishonorable discharge, which is sort of what I suspected. Most of the media don’t understand the difference between the two, and dishonorable discharges are pretty rare. Bergdahl aside, I didn’t think dishonorable discharges unaccompanied by a lengthy prison sentence were common.
The BCD would not prevent him from owning a gun. However, it was still illegal for him to possess a gun under either 922(g)(1) or (9) because he was convicted of either a felony or a misdemeanor of domestic violence.
Read the update.