To me, it said that the defendants were illegally transporting a weapon.
The defendants claimed that their 2nd Amendment right allowed them to do so because any law saying it was illegal to transport weapons would be un-Constitutional.
So the USSC said that the 2nd Amendment did not mean that you could transport any weapon, any where, without following the federal and local restrictions on such transportation.
Specifically, in this case, a sawed off shotgun being transported across state lines.
No where in that link do I see anything saying that private ownership is NOT a right specifically stated in the Constitution.