More to the point, I think, is that there was no record of any testimony or evidence presented that a sawed-off shotgun had NO military use. The burden would have been on the prosecution.
The alternative is to believe that failure to defend oneself adequately is grounds for remand from the Supreme Court or that a person who keeps and bears arms is guilty of a crime until proven innocent. The latter case applies to Kalifornians today.
The Supreme Court did not uphold the conviction of Miller or his co-defendant Layton, because they were never convicted. All it did was rule that the government could put forth a case against them, and that if they wanted to claim Second-Amendment protection they would have to (in the upcoming case) present evidence that a shotgun was militarily useful.
Had the government sought a conviction following U.S. v. Miller, the surviving defendant (Layton) would have had the right to introduce evidence in court that a shotgun was militarily useful. The government basically dropped, the case, however, so Layton had neither the need nor opportunity to present such evidence.