Oil Medium Solar Stove

I had a crazy idea this evening on the way home and I'm hoping you guys can help me sort out whether it's crazy awesome or just plain nuts.

Is there any reason one couldn't construct a solar 'oven' filled with oil as thermal mass, pretty well insulated everywhere except a cooking surface on top?

Is there any reason [safety perhaps?] this would be a better idea than using concentrated solar to heat the pot/skillet [perhaps reflected off a lower surface to get the heat onto the bottom] directly?

As a final note for clarification, the oil I have in mind is tallow or lard, certainly not a non-foodsafe oil [I include your standard vegetable/seed oils in that] or one that smokes at low temperatures [such as olive oil]

Solar ovens do their best to make use of a barely adequate heat source. They gather energy and do their best to keep from losing any while it transfers to your food. Energy used heating the oil isn't heating your food. Lots of thermal mass would be good for a long slow cook but solar ovens already cook like that.
What solar ovens lack is the kind of heat you need to fry things. I'm thinking an old satellite dish would make a great solar cooker, something around 3 ft diameter. Point it at the sun with a pot near where the dish pickup would be.