You have that backwards. Radiation follows the inverse square law. The further away the object, the less a difference there is by a factor of the distance squared. So at very close distances, which is where these pockets are, the difference between aluminum and stone is huge.
Wait a sec. Radiative impact is decreased as you move further away. Shiny materials create a barrier to emission. As you move closer, that barrier should become less significant because of the increased radiative impact. Am I missing something? Are you saying that if I have a shiny radiator and a black radiator, if I hold my hand far enough away, the heat will feel comparable, but if I move my hand closer, the poor emissivity will kick in and cause my hand to feel proportionately cooler? The closer my hands gets to the poor emitter, the more proportionately cooler it will feel?
While we're on the topic of radiation...
I'm curious, are better conductors more powerful/faster emitters? In, say, a typical 550 degree environment, would a pre-heated slab of steel brown a pizza from above any better than a firebrick?
My gut feeling is that steel's superior conductivity will cause it to lose energy faster to the air around it. It will glow (in this instance non visible IR) more intensely for a shorter amount of time than the firebrick. Assuming that that 'shorter amount of time' is the time it takes to bake a pizza, shouldn't the pizza brown more under the steel than under the brick?
For the sake of argument, let's assume the brick and the steel are the same color.