Jesus was a Palestinian?

It seems strange for the PLO to be claiming Jesus as a Palestinian. It brings forth the following points. There was no such place as Paletine during Jesus's time as there is no such country now. The area was named Palestinie by the Romans to get rid of the Jews - in the same way that the Arabs are now claiming the existence of a state of Palestine to get rid of the Jews. In Jesus's time the area was run by Jews and called Judea. Israel is its successor. it is interesting to note that Jesus was born in Bethlehem and spent time in a united Jerusalem, which would indicate that the West bank was part of what was then Judea and should be part of its current successor, that is, Israel.