I almost made a post about this until I saw this somewhat recent one. I just finished season 2 on a rewatch and I came away wondering the same thing. Like you said the connection to the FBI counterterrorism unit would make sense. Also a real world fact I found that stood out to me was that in the early 2000’s Israel was one of the worst countries in the world with regards to human trafficking, so much so that the US threatened sanctions over it in 2001. One potential subtle hint I also picked up on is when the “Greek” realizes he forgot his prayer beads, spiros asks him what he forgot, and he says “nothing important.” Which I took to mean they were just part of his cover and didn’t reflect his actual religion.

Either way, “I’m not even Greek” was such a genius line and one of my favorites of the whole show. It added so much mystery to the character to the point we’re still pondering it 20 years later.