No, the Book of Mormon says that Jesus would be born at Jerusalem, not in Jerusalem:
10 And behold, he shall be born of Mary, at Jerusalem which is the land of our forefathers, she being a virgin, a precious and chosen vessel, who shall be overshadowed and conceive by the power of the Holy Ghost, and bring forth a son, yea, even the Son of God. (Alma 7:10)
As you no doubt are aware, the preposition at can mean "near." Bethelehem, being about six miles from the center of Jerusalem, certainly qualifies as "near Jerusalem."
Let's see...Bill Clinton parsed the word "is" --- and now you're parsing the supposed "distinction" between at or in.
But thank you for chiming up. 'Cause you made my point, which is, that per Mormon apologists, if a Mormon (or anyone) taking this survey answered "Jerusalem" -- one of the choices on this multiple-choice survey -- then they would be "correct."
I mean, what? They did a survey where answering either of two cities was the "correct" answer per your apologetic? So, yes or no, answering either of two answers was "correct?"
Thank you Bill Clinton!