U.S. Customs and Border Protection in a posting dated June 21, 2016 is clear:
travelers in the following categories are no longer eligible to travel or be admitted to the United States under the VWP:
- Nationals of VWP countries who have been present in Iraq, Syria, or countries listed under specified designation lists (currently including Iran and Sudan) at any time on or after March 1, 2011 (with limited government/military exceptions).
- Nationals of VWP countries who have been present in Iraq, Syria, Iran, Sudan, at any time on or after March 1, 2011 (with limited government/military exceptions).
Your husband works for an oil company and worked on a land rig Sep 2013 for just less than 2 wks. Clearly he does not fit the "government/military" exemptions (ibid):
These restrictions do not apply to VWP travelers whose presence in Iraq, Syria, Iran, Sudan, Libya, Somalia, or Yemen was to perform military service in the armed forces of a program country, or in order to carry out official duties as a full-time employee of the government of a program country.
If he wants to be allowed to board an aircraft going to USA he will have to apply for and obtain a visa. Yes, it is a big nuisance, and some cost, for someone residing in Aberdeen but (a) not very different from the requirements of some other countries and (b) not very different from the requirement for some non-UK nationals seeking to remain resident in Aberdeen.
Can I visit the US under the terms of VWP after previously being in Iraq for business?
With an ESTA you can (unless you too have been to Iraq on business recently), your husband can't.