There was already evidence, though none presented in court, that a sawed-off shotgun has military application. "Trench guns" were used during WWI and, AFAIK, were in the Army's arsenal at the time.
Of course there was, but the Supreme Court ruled that the lower court should not have taken judicial notice of that evidence without it being presented in Court. The case had been thrown out before the trial, based on the Unconstitutionality of the law. The Supreme Court overruled that and returned the case to the lower court for further proceedings. However by then Miller was dead, found in a creek with his 1911, with some rounds fired. His partner had plea bargained for a lessor charge, and thus no further proceedings were held. If they had been, such evidence could have been presented in, or in support of, a new motion to throw out the indictment.
IOW, Miller is a darn thin reed upon which the massive edifice of modern gun control us built, at the federal level at least.