Book of Mormon Context: The admonition to total honesty in one’s relationships was as applicable to the Nephites as to the Israelites—and as it is to the modern world. The specific examples rely upon rabbinic traditions well known in the Old World; probably exact parallels did not exist in the New World. Even assuming a parallel development of legalism in oaths, the items upon which the oaths would have been taken would have developed in a different environment. For example, deleting an oath on Jerusalem makes sense, and the reasoning for its deletion would probably apply to the other examples as well.
Like other textual alterations, these change show Joseph’s translation process, not the underlying plate text. The essential meaning shines through, but it does so through the extra layer of the Matthean redaction upon which Joseph made his own alterations.
Reference: This passage may allude to Psalm 50:14: “Offer unto God thanksgiving; and pay thy vows unto the most High.” While the parallel is not close in the King James Version, the two passages are nearly verbatim in the Greek Septuagint.
The emphasis is paying/fulfilling oaths or vows to God. James 5:12 echoes the Sermon on the Mount’s prohibition against swearing: “But above all things, my brethren, swear not, neither by heaven, neither by the earth, neither by any other oath: but let your yea be yea; and your nay, nay; lest ye fall into condemnation.”
Comparison: There are two changes in this passage. The first changes “saying” to “written,” as in the other 3 Nephi passages. The second removes “neither by Jerusalem; for it is the city of the great King” from Matthew’s verse 35. Obviously it was not relevant to the Nephites, who also had a city named Jerusalem but which was hardly sacred or important (Alma 21:1–4).