Independent? The U.S. Military casts a shadow over them all.
Who can come and go - when and where? - all the Arab countries I named are independent. The US doesn't decide who enters and leaves those countries.
Ah, what would being INDEPENDENT actually mean to tribes with differing religious loyalties and blood relations? - ok, consider one of the countries on my list: Jordan.
Jordan is ruled by King Abdullah, a Sunni Muslim who is a Hashemite, i.e. he claims he is a descendent of Prophet Muhammad. He rules over Arab Bedouin and Arab Palestinians (both Sunni Muslim), and minorities, such as Christian Armenians. King Abdullah is on record as saying all Jordanian citizens are equal citizens, the one proviso being that it's illegal for Christians to proselytise. Any Muslims who leave the faith must do so very carefully. As for any Muslims who are Sufi - I don't know about them.
Despite these points, Jordan is a relatively rich, prosperous, stable country. The US doesn't rule the country; King Abdullah does.
Lebanon is even more diverse, with different faiths and minorities being guaranteed a number of seats in the Lebanese Parliament. Again, Lebanon is a relatively stable country.
I think, Terry, that you're conflating influence and control - yes, America is a big player in world politics and so exerts some influence on many countries. But that's not the same as the US controlling those countries - those countries (the Arab countries I listed) still retain their independence.