The Palestinians had accepted Israel's existence.

True, they did, the pragmatics did, but not Hamas, not the Islamic Jihad and not other rejectionist factions, which all together make up half of the Palestinian people. As for the “moderate” they had indeed accepted the FACT that Israel exists. But did they accept the RIGHT of that FACT to exist?
When it comes to Palestinian propaganda, beware of words added and words omitted. And here the omitted word is 'RIGHT'. Even as recently as early 2009 Palestinian President Mahmood Abbas refused to accept Israel as a Jewish state.