I don't think you can consider that Western managers in general don't use arrogance as a blocker based on just one incident. We however might have differnt perceptions of what is arrogant.
Yes some people only care about a technical ability, others care for much more than that. In general people who have been forced to work with a jerk tend to care more about personality than those who haven't or who were above the jerk in the organizational chain. So a manager who has never been part of a dev team except as a manager may have more tolerance than those of us who have seen how the dynamic affects everyone. Further, since the American team did a non-technical interview, it is likely that he came across as less arrogant to them.
I have done a lot of interviewing for different types of jobs including developers and in every case, the panel (I have always interviewed as part of a panel) rejected the arrogant person unless there was literally no one else in consideration who could also do the job. In no case was arrogance the documented reason why we rejected the person. Generally it could be a case of these 4 people are qualified and we choose this one for his better fit with the team.
However, your real problem isn't this guy as he didn't pass the technical. Your real problem is convincing your American team that there are cultural differences that you want considered as part of the hiring process and why.
Americans in general are not very aware of how other cultures work as many of them have never left the US. Culturally what you see as arrogance might not even be perceived as such in the US. In general we are much more blunt than many other cultures.
However, the person will have to work with your team in your country. I think this is the point you need to make to the American manager. You will not hire someone technically unqualifed, but you also will not recommend for hire somone who will not fit well into the team culturally as your culture perceives it. For employees who will be physically located in the Middle East, the Middle Eastern team should have the final say.
At the very least, you need to get the American managers to agree that both groups have veto power. Anyone that either group does not want is out. Then of the ones left, the Americans can choose the final candidate. All of you will have to work with the people you hire, all of you should have veto power. Perhaps you could set things up in the future so that they only interview the people your team is willing to work with. If you tell them that this will save their valuable time it should help convince them. Then you simply don't send them any candidates to interview that you think won't fit in culturally.
Addressing the cultural differences is one thing you will need to learn to be able to work well with the Americans. I don't know what specific country you are from, so the cultural differences are hard for me to address in this. However, the book, Speaking of India, (http://www.amazon.com/Speaking-India-Bridging-Communication-Working-ebook/dp/B004AE3R3O/ref=sr_1_1?ie=UTF8&qid=1405618146&sr=8-1&keywords=speaking+of+india) has a good discussion of how American managers think which might help you figure out what cultural differnces you need to to discuss with them.
I know I found it very helpful in learning to work with Indian developers and some of what is there might be applicable to your culture as well (As some will almost certainly not be). If you can find an equivalent book on doing business in your part of the world, recommending it to your American colleagues could help. If not, you could use this book as a starting place to figure out the cultural issues you want to address and explain.
One thing I highly recommend when starting to work with people of another culture is to get them physically together for at least a few weeks. I know some of our Indian devs didn't really believe that Americans could possibly think the way they do until they saw it for themselves. I know the ones we have brought to the US for a few weeks of training have been the ones that have most effectively learned to deal with the cultural divide.