"Palestinian"? "Jordanian"? "Ottoman"? or "Israeli"?

This snippet is from the Israel Policy Forum, close to Obama, formerly close to Ehud Olmert (his "we are tired" speech was made to them):

The Shepherd Hotel sits in Sheikh Jarrah, a predominantly Palestinian neighborhood that also contains foreign consulates, such as the British embassy, and Israeli government buildings.

Irving Moskowitz, a Miami-based millionaire who has supported numerous Jewish building projects in East Jerusalem, purchased the Shepherd Hotel in 1985. From 1987 to 2002, Moskowitz rented the building out to Israel’s border police until Israel granted him permission to construct a housing development.

Moskowitz’s goal is not to construct housing for its own sake, but rather to change the facts on the ground and ensure Israeli control of a neighborhood that is overwhelmingly Palestinian. The Palestinians understand Moskowitz’s intentions and voiced their protest to the United States. Their fear is that they will lose yet another East Jerusalem neighborhood to Israeli settlers.

"Palestinian"?

And during 1948-1967, it was...Jordanian?

And during 1918-1948, it was...Palestinian?

And during 1516-1918, it was...Ottoman?

Or perhaps, just plain Arab?

Because, if not, shouldn't we say that it is "Israeli" between 1967-2009?

Why does it change under other rulers but not when Israel rules the city?