Actually, actually, the Court made some comments and remanded the case. My reading of their decision is consistent with the idea that the lower court which ruled that the Second Amendment protected the defendant should offer the prosecution the opportunity to continue with their case, but that the PROSECUTION would have to prove that the shotgun is NOT suitable.
How could there possibly be such a burden on the defendant? Next we would have people charged with bank robbery forced to prove that their withdrawal was from their account or people charged with murder forced to prove that the "victim" died of natural causes.
I've not read the briefs in Miller, but I would expect the prosecution would have made a prima facie case that sawed-off shotguns weren't "militia" weapons. If not, they certainly could have done so easily. The burden would then have been on Miller/Layton to rip that prima facie case to shreds, which they too could have done easily.