Sociological: How is it that the two people know so much about each others genealogy so quickly? Precisely because this was of extreme importance. Sorenson discusses the principle of kin interactions for a later Book of Mormon event:
"…when Alma had approached him, Amulek identified himself as a "Nephite" (Alma 8:20). "I am Amulek . . . a descendant of Nephi," Alma 10:2-3 reports him saying. Mosiah 17:2 gives Alma's descent in identical language. We understand, then, that the two were establishing that they belonged to the same lineage. A Mayan practice at the time of the Spanish conquest shows the same principle governing how to get along in strange territory: "When anyone finds himself in a strange region and in need, he has recourse to those of his name [kin group]; and if there are any, they receive him and treat him with all kindness." (Sorenson, 1985, p. 212, citing: William A. Haviland, "Principles of Descent in Sixteenth Century Yucatan," Katunob 8, no. 2 (December 1972):64.).
It is therefore quite understandable that one of the first "orders of business" with the newcomers straggling in out of the wilderness would be to examine genealogies to see if there were any kinship obligations between them. What they found was not only a kinship, but one of utmost importance as the tie returned to the origins of both groups in Jerusalem, which by now must have been nearly the stuff of legend and myth.
Having thus established an important bond linking them both to a common sacred origin, the ties of kinship took over, and Mosiah's people were welcomed - with rejoicing.