Yup, what everyone else said: rust is fine. At least it's preferable to chunks of chrome coating :)
Argentine grills are not coated. If you want to keep them from rusting, you just grease them a bit with the remains of the meat (you usually don't even need to do that) and clean them up next time around. If you are really concerned about the rust, you can always coat the grill with vegetable oil (just take a paper napkin, soak it in vegetable oil and lightly rub the grill with it.)
BTW, the biggest unrelated tip: when you are seasoning meat, use kosher salt instead of fine salt. It works much better!
you "treat" the metal much like you would a cast iron skillet.
After using, clean the grill, rub a thin coat of oil (I use canola different oils provide different seal quantity) then heat to smoking point. Wipe down and repeat a few times. This will coat the metal.
Most importantly DON'T use detergents it'll ruin the seal
It is always an after thought, you finish cooking and the grill is super hot from the charcoal. Its late at night, you want to eat and relax. By the time the grill cools, you are sound asleep.
Actually trivalent chromium is an essential nutrient (trace amounts). Hexavalent chromium is the "bad" chromium. Chromium metal is not considered a health hazard.
Chromium salts (chromates) can cause allergic skin reactions.