This Fly Dubai flight is a contractor milk run connecting in DXB with the evening international departures. You run into a lot of these folks in business class going home on leave or at the termination of their contracts.
On the aviation side, many of these contractors were employed in the past by OGA's, Once Great Airlines. Kinda like some of us here, come to think of it...
given the recent "improvement" in US/Iran relations I doubt this incident will be difficult to resolve.
Fly Dubai isn't an American carrier but U.S. carriers have been quietly flying through Iranian (and North Korean
) airspace for years.