Even though the boy’s identity can’t be determined with total certainty, his story does seem to confirm that he is indeed Adam. If Adam did fall down the mineshaft but was only injured, it makes sense that he’d remember coming to in the dark and crawling out of the shaft to safety. The ways in which Adam has been trying to survive demonstrate his complete isolation from society. While in his “real” life, he was simply socially isolated from a few of his peers, in this version of his life, he is completely cut off from all of society and all of his own memories, too. Symbolically, the barely-edible things he’s been eating highlights this total isolation; while Phil isolates himself with sweets and snacks, Adam is even more deeply separated from the group.