Child welfare groups expressed outrage over Friday's attempt, saying some of the children had parents who survived the Jan. 12 earthquake.
An Associated Press photo taken Saturday, as the Americans posed at police headquarters at the airport in Port-au-Prince, included 47-year-old Jim Allen of Amarillo.
The Amarillo Globe-News reported Monday that Allen was joined in Haiti by his cousin, Paul Thompson, formerly of Amarillo, and Thompson's son, Silas.
The Baptist group's "Haitian Orphan Rescue Mission" was described as an effort to save abandoned, traumatized children.