slamfire, I have to disagree. I have seen an awful lot of potatoes growing in several countries (not, admittedly the USA) in the last few years, and EVERYBODY still grows them underground. A straw or hay mulch would let light through and that is what turns the potato skin green. Obviously a commercial scale grower could not afford to take the risk. They might well mulch in areas where they get late frosts because the shoots would get some protection from the mulch, but the seed will still be planted below ground. A black heavy plastic over the top of potatoes laid on the ground, and then a mulch, is a possibility, but only practical on a smallish scale.
Green potatoes are sound inside, but never ever eat one. Either keep it for planting or dispose of it - and not to your pet pig because they are just as poisonous to livestock. Old McDonald.