Knight Ridder Newspapers reported that Berg told friends in Iraq that Iraqi police arrested him because he had a Jewish-sounding last name and an Israeli stamp in his passport.
I don't know about private citizens but Government contractors, civil service, and military that have Government passports have two passports if they travel to Israel and the rest of the Middle East as they don't want to have a passport with an Israeli stamp if they are traveling to Saudi or other ME countries.
My husband used to work for AFMC's Contract Maintenance Center back in the late 70's and he had two passports for that reason. According to someone I just asked, the same is true today.