There is a New York Times article about how the patient caught the disease:
"Mr. Duncan, the first person to develop symptoms outside Africa during the current epidemic, had direct contact with a woman stricken by Ebola on Sept. 15, just four days before he left Liberia for the United States, the woman’s parents and Mr. Duncan’s neighbors said.
In a pattern often seen here in Monrovia, the Liberian capital, the family of the woman, Marthalene Williams, 19, took her by taxi to a hospital with Mr. Duncan’s help on Sept. 15 after failing to get an ambulance, said her parents, Emmanuel and Amie Williams. She was convulsing and seven months pregnant, they said.
Turned away from a hospital for lack of space in its Ebola treatment ward, the family said it took Ms. Williams back home in the evening, and that she died hours later, around 3 a.m."
The question arises if anyone bothered to ask him if he had any contact with anyone with the disease (I think I read there was screening both in Liberia and in the U.S.) or if he was asked and lied.