Through this period, no Jewish claim was made to the land, which remained for the most part, majority Arab. And you are in fact incorrect, The last Crusader stronghold of Acre fell to Muslim armies in 1291, and in reality, by 30 years before that, the vast majority of Palestine was in the hands of Muslims, excepting a few walled cities.
Saladin was indeed a Kurd, not an Arab, Kurds are most closely related to Persians, since they are an Iranian people, but they have a closer relation to Croats or Germans than they do to Jews. Nevertheless, his dynasty was superceded by the Mamlukes by 1260.
Arabs had the majority population there until recently, and had ruled it more recently. It doesn't matter that the Arabs did not actually control their own state there when it was given to the Jews, if that was the case, Belgium could have done whatever they wanted with the Belgian Congo, including use it as a gigantic slave labor camp or for that matter, give it to X group to settle, since they were granted the land via a treaty.