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IMO, that's why the Palestinians need to 'think outside the box' and temporarily turn into Finns. Or at least make a concerted effort to show the U.S. (and the Israelis) that they can act with total restraint when necessary.
This would drive a stake through a devestating meme that has been allowing the Isaeli governments to not negotiate with the recent Palestinian govts.
The meme is: 'The Palestinians are barbarians who if we gave them their precious state would immediately begin plans for turning Israel into Greater Palestine'.
That one dovetails with another meme: 'The Palestininan leadership can't control their population at all. If we gave them their state, they would be ineffectual in stopping any rogue elements from continuing to harass Israelis (who would now be all in Israel proper)'
The above one says you can't take your boot off their neck, because they'll keep on fighting you & if they're going to do that you (Israel) are in a stronger position (militarily) if you are occupying them.
Given how the Palestininan leadership has acted in the last several years, I can understand how the above conjectures are believed by a significant portion of the Israeli (and American) public.