That person would be incorrect.
The sermon on the mount was not a "law", let alone a "higher law".
Your comparison is incorrect. Christ pointed out the false teachings by the Pharisees that had crept in over time. LDS doctrine is not pointing out the false teachings of Christianity over time. It is introducing false teachings under the guise of "revelation" by a false prophet(s) and those who follow him/them. In your example, it would be like the Jews trying to teach Jesus that his teachings are the false ones.
This is what Jesus taught about the law when He gave us the sermon on the mount:
(New Testament | Matthew 5:27 - 48)
27 ¶ Ye have heard that it was said by them of old time, Thou shalt not commit adultery:
28 But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart.
29 And if thy right eye offend thee, pluck it out, and cast it from thee: for it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell.
30 And if thy right hand offend thee, cut if off, and cast it from thee: for it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell.
31 It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement:
32 But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
33 ¶ Again, ye have heard that it hath been said by them of old time, Thou shalt not forswear thyself, but shalt perform unto the Lord thine oaths:
34 But I say unto you, Swear not at all; neither by heaven; for it is God's throne:
35 Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King.
36 Neither shalt thou swear by thy head, because thou canst not make one hair white or black.
37 But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil.
38 ¶ Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth:
39 But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also.
40 And if any man will sue thee at the law, and take away thy coat, let him have thy cloke also.
41 And whosoever shall compel thee to go a mile, go with him twain.
42 Give to him that asketh thee, and from him that would borrow of thee turn not thou away.
43 ¶ Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy.
44 But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;
45 That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust.
46 For if ye love them which love you, what reward have ye? do not even the publicans the same?
47 And if ye salute your brethren only, what do ye more than others? do not even the publicans so?
48 Be ye therefore perfect, even as your Father which is in heaven is perfect.
This is definitely a higher law than the mosaic law.
