Wouldn't cloud cover just cause the heat energy to be absorbed by the clouds or reflected back to a much larger area of the ground (so only a small percentage would return to the device itself)?
I agree that the common explanation is confusing. If I understand it right, it's not the transparency of the sky to the outgoing radiation that matters, but the absence of a (relatiely) high temperature emitter like a cloud. The two are closely tied (if there is no absorber, then there is no emitter) but the "clear sky" explanation mixes up cause and effect.
Rather than emphasizing the transparency, a clearer explanation would emphasize the absence of a counterbalancing warm mass whose emissions can be absorbed. Objects are always losing energy by black body radiation, but normally are gaining thermal energy from their similarly temperatured environment. One a clear night, there is a greater imbalance.
Wouldn't cloud cover just cause the heat energy to be absorbed by the clouds or reflected back to a much larger area of the ground (so only a small percentage would return to the device itself)?