I doubt theres even a grain of truth in the story, while it's possible that some "Palestinians", the problem is "Palestinian" refers to people of Arab descent. The problem today is that Arab is no longer used in a racial sense but anyone can literally be an Arab. In the case of a North African, a person from the Levant, or Saudi Arabia, they would all be considered Arabs which means it's a "identity" issue more than a ethnic issue. That esentially means if you lived in an "Arab" country, adapted the cultures, spoke Arabic and converted to Islam, you would esentially assume Arab identity.
What is not mentioned is that during the 1920's to 1940's, 50,000 Arabs "immigrated" to what was then known as the "British Mandate Of Palestine" to combat Jewish immigration from as mentioned, Egypt, North Africa, Saudi and other Arab countries but were also used as work force in many cases. As a result, you can see a difference in appearance from "Palestinians" in both Gaza and West Bank.
Therefore is it possible some Arabs or "Palestinians" are descended from the original Israelites and Jews? Sure, same way that the majority of the Berbers/Amazigh converted to Islam and assumed Arab identity (believe it or not, Arabs are not the majority in North Africa racially). Same concept how many Mexicans are of mixed Spanish/Indegenious blood but have assumed the politics/language/religion of the Spanish.
They have basically thrown away their identity, culture, language, religion to assume a foreign identity and make up a very tiny number at that. The majority of the Jews however do show a trace to the region, granted Arabs never mention that the Sephardic make up a large portion of the population which they may have similar genetics to the Arabs but do not identify the same or assume the religion of the Muslims.