One more thing to add, re:
2. Secondly, birds have the ability to see in the UV spectrum and the ignorance of that basic fact renders moot any conclusions about what birds actually see in this instance.
Check this out:
Majerus M.E.N.; Brunton C.F.A.; Stalker J.
A bird’s eye view of the peppered moth. Journal of Evolutionary Biology, Volume 13, Number 2, March 2000, pp. 155-159(5)
...One important aspect of early work evaluating the relative crypsis of the forms of B. betularia on tree trunks with different lichen flora was the reliance on human observers. Humans, however, do not have the same visual capabilities as birds. Birds have well-developed ultraviolet (UV) vision, an important component of their colour processing system that affects many aspects of behaviour, including prey detection. We examined the UV characteristics of the two forms of B. betularia and a number of foliose and crustose lichens. In human visible light the speckled form typica appeared cyptic when seen against a background of foliose lichen, whereas the dark form carbonaria was conspicuous. Under UV light the situation was reversed. The foliose lichens absorbed UV and appeared dark as did carbonaria. Typica, however, reflected UV and was conspicuous. Against crustose lichens, typica was less visible than carbonaria in both visible and UV light. These findings are considered in relation to the distribution and recolonization of trees by lichens and the resting behaviour of B. betularia.
There have also been studies showing that these moths do rest on tree branches during the day, and that they preferentially choose resting locations where they camouflage well. I can provide citations if necessary.