As violence spread across Iraq during Secretary of State Condoleezza Rice's visit to the Middle East this week, kings, presidents and prime ministers told her that they were concerned that sectarian violence could spread across the Middle East. "It came up pretty much everywhere," said a senior State Department official traveling with Ms. Rice. During this trip, Ms. Rice met with leaders of Egypt, Saudi Arabia, Lebanon, the United Arab Emirates and the other Persian Gulf states. One of the senior officials traveling with Ms. Rice said the Arab leaders, in their conversations with her, were particularly concerned that "outsiders...