There seems to be confusion about absolute and relative losses.
Maybe this will make things clearer...
A naked person in still air loses (depending on the experimental conditions) 50% to 80% of their body heat by radiation. The absolute amount is of the order 100 Watts by radiation, the remainder by conduction and convection.
Now lay that person down on the cold ground. They will now be losing somewhere of the order of 400 Watts or more by conduction with the ground if the ground is at, say, 40F. So even though they are still radiating 100W, that is now a much smaller proportion of their total heat loss. So when a person is laying on the ground, it's much more important to deal with the conductive heat losses before worrying about the radiative losses.
As soon as you add moving air (increasing convective losses), clothing, the layers of sleeping bag, mat, etc. into the equation it all gets complicated of course, but clothing reduces radiative losses too. The essential point is this: in real world conditions, radiative losses are (relatively) small. For most purposes, you are best to focus on reducing heat lost by conduction and convection.
Hope that helps.