The origins of this lie can be seen in this 1951 UNRWA report:
The desire to go back to their homes is general among all classes; it is proclaimed orally at all meetings and organized demonstrations, and, in writing, in all letters addressed to the Agency and all complaints handed in to the area officers. Many refugees are ceasing to believe in a possible return, yet this does not prevent them from insisting on it, since they feel that to agree to consider any other solution would be to show their weakness...Palestinian Arabs have always been sensitive to publicly adhere to the "politically correct" idea that they will not accept any solution besides "return." Westerners who spoke to them were impressed with this seeming determination and would report this as fact. This idea was pushed by self-proclaimed leaders (as this report indicates) making any Palestinian refugee reluctant to publicly oppose it. (Within a few years, UNRWA itself would have its teachers continue this insistence on "return" at the expense of solving the refugee problem - a form of job security.)
However, every time the opportunity arose, individual Arabs would invariably choose to become citizens of their host countries and would go to great lengths to obtain such citizenship. The worry about showing "weakness" was a concern for the Palestinian Arabs as a group, but each one individually seems to be eager to better their lives by becoming citizens wherever they can.
Last year, Egypt finally started implementing a 2004 law saying that children of Palestinian fathers and Egyptian mothers can become Egyptian citizens. Tens of thousands of Gazans started applying for citizenship, going back generations to prove their Egyptian parentage - and against the public pronouncements of their "leaders." And every few months, a few hundred Gazans would get their prize - Egyptian citizenship and an opportunity to stop being treated like dirt by the entire Arab world. So far between two and three thousand Palestinian Arabs have been able to become citizens of Egypt.
Today another 680 Palestinian Arabs became Egyptian citizens.
Given the choice, almost every Palestinian Arab would choose to become naturalized in any Arab country.
But they would all keep telling credulous Westerners the opposite.
They are afraid to say the truth publicly because it contradicts everything their leaders - and other Arab leaders - have been saying for decades. Publicly opposing the politically correct line of insisting on "return" is dangerous. So they say one thing and act the opposite way, and no one is the wiser.
And their human rights are being trampled by the Arabs who pretend to love them.