For some environments choosing is mute, moths living on sand dune or beaches have no need to choose (as long as they don't rest on plants); for moths living on peaty soils choosing is not needed; similar situation for moths living of chalk.
However, for moths that match a specific piece of background it would seem that choosing the correct background would be essential for survival. Several of the Fall-flying moths have the colour of dry leaves, it would be critical for such individuals not to rest on any contrasting background.
I run a moth light trap most nights, moths trapped alive in a large plastic box with screen sides for the moths to rest. This am (31x19) there were 3 dark moths resting on the white screen (not cryptic!). On the bottom of the trap there was one dry white birch leaf and resting on it was a Straight-toothed Sallow (Eupsilia vinulenta). Appears to me to be an example of a cryptic moth selecting its resting background.
