Well, since it's safe to assume that Joseph Smith, being brought up in a very religious family and having read the Bible regularly and interested in matters of Christianity, knew full well that Jesus was born in Bethlehem, the question to ask then becomes, why did he say At Jerusalem instead of the obvious Bethlehem?
The next question to ask then becomes, why haven't you asked the first question?
Why did Smith say "At Jerusalem" instead of Bethlehem as the birthplace of Jesus when he was supposedly delivering the true word of God from the Holy Spirit?
Obviously because he was not delivering a true revelation of God.
God ties things up for us. He is the God of all history. His word is forever. He would never make such a drastic error -- with all its Old and New Testament implications of such an error. Jerusalem is quite a big difference from the little town of Bethlehem.