The peanut farmer doesn't explicitly write it in so many words, but that's the clear meaning of the following from Carter's book:
"Damascus and then Baghdad and other cities became the dominant centers and Arabia was relegated to a mere province, its remaining importance being as the site of the two holy cities of Islam, Mecca and Medina."
Carter didn't write "two of the holy cities of Islam" or even "two of the three holy cities of Islam;" he clearly acknowledges there are really only two truly holy cities in Islam, Mecca and Medina. Jerusalem simply isn't on the radar.
This is one of a number of instances of Carter accidentally telling the truth and undermining his own basic anti-Israel message.
It's no accident that Jerusalem isn't mentioned in the Koran; it's just not important for Muslims.
One of the litmus tests for recognizing when the Arabs are ever getting serious about living together in peace is when they stop insisting on the redivision of Israel's capital, a city they have always ignored when it hasn't been controlled by those they consider infidels.