If he really wants to be anonymous I suggest you research more the Namecheap situation, ask them questions about how private they really are, etc. And if they are in US, doesn't that mean they are subject to the Patriot Act and national security letters, too?

This doesn't necessarily mean a foreign domain registrar would be much more private either. At the end of the day it will depend how good their relationship with US is. But there might be some countries like Iceland or others who care more about this. I mean if you really want to be extreme about this and not take any chances.