The belt clips around the cases are steel, and could have left rust dust on the cases. The cases themselves have not rusted.
Click on the link to the high-res photo, and you'll change your mind. The brass and the copper(?) jackets on the bullets have that distinctive blue corrosion on them.
The gun itself looks pretty beat up, too.
But they have corroded. You can see the green patina that corroded develops after some time exposed to the elements.