I also find it funny that people are picking apart the emissivity differences between the shiny and dull side of an incredibly conductive material that is radiating the heat of the food to the surrounding air. If keeping things warm is your goal, foil is not the right choice... plastic and glass are insulators and are your best options.
Foil is good once you're done with the food and are storing in the the fridge, because the conductive aluminum helps it get to safe refrigeration temperature faster. Or if you're grilling something in the foil, for the same reason. There are lots of good uses for foil, but heat retention is not one of them.
In the vast majority of times that I've seen this question asked, they are cooking an item. Foil is often perfectly fine for cooking. It helps conduct heat more uniformly around the surface, can withstand the high temperatures, can keep the moisture in, etc. They usually aren't concerned with keeping things warm, but instead with getting them warm.
In that case, they are worried about reflecting the radiation from the oven AWAY from the food. Thus, you want a high thermal emissivity so that the radiant heat helps cook the food rather than just reflect it away.
The dull side has a negligibly higher emissivity than the shiny side, so people mistakenly think it matters. It does not. The difference is negligible and you get a bigger difference depending on how many crinkles you have in the foil (which no one asks about) than the side of the foil to use (which keeps being questioned). And even then the difference still so small that it doesn't matter in cooking.