The feature size of the matte vs shiny sides are much smaller than the wavelength of the bulk of the radiated light in either a microwave or conventional oven.

No. Aluminum foil has the same material properties with respect to convection and conduction of heat no matter which side faces out. The only heat that would be different would be radiated heat, which your food won't have a ton of, and even then, the dull side is still quite reflective. It's maybe one of those "technically" correct statements that the shiny side reflects more heat, but for the application of cooking, the impact is effectively zero. The retention of steam is going to be such a larger factor the side you use will effectively make no difference.

The shiny and dull sides look like perfect mirrors in IR wavelengths.

I recall similar advice around mylar heat blankets. Perhaps those got mixed up?