[ImJustAnotherOkie]

Categorically false if you’ve ever been camping and made a foil dinner.

If the shiny side is facing outward the food will take significantly longer to cook.

Dull side reflects less heat and lets the heat in and the shiny inside keeps the heat inside cooking the food.

I know that for a fact.

[Weirdad]

I think that has merit.

Varies with whether it is in coals or similar (contact heat transfer) or heated by radiated heat. The shiny does reflect radiated heat a bit better

I also think that the dull side is a little more likely to leach aluminum into food, especially more caustic foods.

Suspect it is not a huge deal either way, however.

Sometimes cooking slower might be good. Sometimes not. People afraid of aluminum might want food on the shiny happy people side.

[LegendHasIt]

I always assumed that too, but never actually compared it....And assumed that it wouldn't make a significant difference; perhaps measurable, but not obvious.... except maybe in a solar cooker.