However, aside from your lack of understanding of location/seperation, you're right. The people who NOW call themselves palestinians have been there for thousands of years. They've been muslims (of one nature or another) for the last 1500, but they've been native to that land for many hundreds of years earlier than that.
Prior to 1881, there were anywhere between 25,000 and 30,000 Arabs in the land of Israel. They lived as good neighbours with their Jewish friends, who were about 4,000 (roughly a quarter, or so), a group of Jews which is reffered to as 'the old settlement', as they never moved from Israel, inspite of all the exiles and all the empires, 3,000 years-worth of them, that tried to capture Israel. As the Jewish immigration began to rise in the late 1800s (due to the rising of the Zionist movement, which called for the establishment of a Jewish state), so did the Arab nations around Israel (which was then called Palestine, due to a practical joke of a Roman emperor) got nervous - namely Jordan, which was, and is still today, a proud monarchy, and a very cautious nation. So, they did what seemed right - and as they couldn't risk open war, as the Ottomans controlled the area, they flooded it with civilians instead. Masses of poor Jordanian Arabs that lived near the border came to (or rather, were pushed into) Israel, to counter the Jewish settlements. They weren't too happy about it, mind you, as there was practically nothing for them here, other than the up-coming strife with the Jewish population.

So, the angry Arabs that now call themselves Palestinians, are those Arabs that came a little over a hundred years ago into Israel. They are misreable, bitter, and have very little hope, and no-where else to go. So, they fight, not yet realising a lasting peace with the strongest nation and also the only democracy in the area could actually benefit them...