Compliance officers are aware that American's Visa Waiver program (ESTA) excludes dual nationals, and individuals who have visited Iran, Iraq, Syria & Sudan. Most compliance officers now routinely initiate enhanced due diligence on potential clients who have ties to these high-risk countries, due to their risk-based perspective.
Now, the Director of Homeland Security United States has added Libya, Somalia & Yemen to the list of countries of concern. You would do well to follow that move by requiring increased compliance measures upon any nationals of those countries, or other nationals who have traveled there, or do business there.
Remember, though the aim of DHS is to identify possible radical Islamists who may have participated in military action in those countries, and are returning to the US, your goal is to rule out potential terrorist financing of new bank customers. The last thing you need, in today's enforcement climate, is a visit, two years later, by law enforcement, and your bank's name on the OFAC "name and shame" monthly of sanctions violators, especially after you learn that your client moved money for an SDGT right under your nose.