According to DNA, Palestinians are more genetically related to Ancient Israelites than any other Jewish group except for Samaritans.
Jews are even less related to Ancient Israelites than all possible Lebanese groups. Why? Because Jews are not pure blood and it undermines the emphasis on the Israelite component of the Jewish identity.
Lebanese and Palestinians could also walk around claiming they are the descendants of ancient Israelites. At least they will be correct in doing so.