In hearing this invitation for healing, the Nephites may have recalled Nephi1’s vision of the Messiah in the Old World performing healing: “And he spake unto me again, saying: Look! And I looked, and I beheld the Lamb of God going forth among the children of men. And I beheld multitudes of people who were sick, and who were afflicted with all manner of diseases, and with devils and unclean spirits; and the angel spake and showed all these things unto me. And they were healed by the power of the Lamb of God; and the devils and the unclean spirits were cast out” (1 Ne. 11:31).
Because the Savior heals, his perception that they wanted him to do what he did in Jerusalem communicates that they were thinking of healing miracles, not other New Testament miracles, such as turning water to wine or withering the fig tree, neither of which had appeared in Nephi’s vision.
Translation: The specific list of illnesses is influenced more by the biblical text than by the historical New World.