You have to travel all the way to Kurdistan to find others like them.
So, yes, odds are there are Palestinians around who can say the place was always "theirs" because, after all, they are the same folks.
This really shouldn't be a surprise to anybody.
Frankly it's about as surprising as discovering the 3,000 year old folk-legends to the effect that the Basque people in Spain and the Irish people in Ireland are true ~ in short, not surprising at all!
Still, given the age of the site, it's entirely possible that the individuals who lived there in that house did not yet end up as universal ancestors to all mankind, but that will, ultimately, happen.
"Very close examination of the "genes" Israeli Jews, Israeli Arabs, and Palestinian Arabs hold in common as "markers" strongly suggest they are all the very same people, and different from those around them."
You are mistaken. Genetic markers (the Priesthood gene) show that Jews from all over the world, Eastern and Western are related. But I know of no study that has shown that Jews and Arabs have genetic markers in common. Most studies show that Jews have remained relatively genetically isolated from non-Jews.
http://www.cohen-levi.org/the_tribe/kohanim_forever.htm
"I once covered a speech by the late Edward Said at UC-Berkeley in which he claimed the ancient people of the Bible who predated the Jews were in fact todays Palestinians. In other words, the Jewish claims to any part of the land of Israel based on the Bible or nationalism should be rejected: the Palestinians were there first. "
http://www.freerepublic.com/focus/f-news/1419428/posts
So is Edward Said the source of your information because you have cited no sources for your contention that:
So, yes, odds are there are Palestinians around who can say the place was always "theirs" because, after all, they are the same folks.