Patrick,
In order to make a conclusive determination, a sophisticated chemical assay would most likely have to be done (and you'd probably have to cut into the sheet metal).
You could try your own "comparative magnetism" test by seeing if the magnetic attraction of a piece of your bright metal against the magnetic attraction of a similar gauge of sheet metal. Is there a painted piece of similar-gauge of sheet metal on your grill assembly? If yes, compare the strength of its magnetic attraction to the magnetic attraction of a bright-piece of your grill.
Magnetic stainless steel would most likely have a noticeably weaker magnetic attraction.
The chrome on my 1954 grill has a substantial layer of copper underneath it. I guess you could try to rub off the layer of chrome (and nickel) but this would mar your grill (and, you would not know how much material to rub/abrade away).
