Nice try but this glossing over doesn't cut it. The Messiah was to be born in Bethlehem. It was a critical component in validating the identity of the Messiah. Reread Mathew 2:3-6 and you'll be reminded of the importance of Bethlehem. If you asked me where the Red Sox baseball team was located and I said Massachusetts, would accept the answer as correct? I doubt it. You'd want me to be more specific because the team is associated with Boston. Just like the Messiah's birth is associated with Bethlehem, not Jerusalem. Glossing over something like this shows a lack of understanding of the importance of true prophecy.
In fact it is a Semetic evidence of the Book of Mormon that such phraseology is used because it was a common near Eastern practice to refer to a town by its regional setting in proximation to a nearby large city.
Or if you apply Occam's Razor, it is much more logically explained as an error in the "most correct book of any on earth."
I understand there were quite a few of them.
I wonder if they got them all...