He says that there are Arab families with the name "Zion" who originally lived on the mountain.
So I researched further and found an article by an apparent member of that family, insisting that it is an ancient Arab name and that there is also a "Zion" castle on the Syrian coast. The Jews, under the name of the Elders of Zion, usurped the honorable Arabic name of Zion.There is indeed a castle in Syria known today as the Citadel of Saladin, but originally called Sahyun, the Arabic equivalent to Zion. It was apparently built by the Byzantines on an old Phoenician fortress site and much enlarged by the Crusaders; I cannot determine who named it Sahyun or when.
Wikipedia notes that while the Mount Zion did apparently have that name before it is mentioned first in Samuel II 5:7, it is pretty clear that the Muslims took the name from the Jews well over a thousand years later, and not from the Jebusites.
In fact, Mohammed referred to the Kaaba in Mecca as "Zion" to supplant Jerusalem as "the new Zion."
It is always amusing to see Muslims - whose religion is based more on Judaism than anything else - claiming that Judaism stole from them.