He boarded in Nigeria and cleared security at that point. They allowed him to board without a passport. What we don't know is whether he had to clear security and immigration in Amsterdam.
It could be that the transfer between planes did not require a pass through Amsterdam immigration. If anyone knows the Amsterdam immigration rules for flights from Nigeria they should let us know. It is a very important point. My personal view is that he could not board a plane in Amsterdam heading for the U.S. without a passport.
I fly international several times a year on Delta. They have always checked for passports at least twice before boarding to the US and sometimes 3 times. I think what was going on here was the lack of a B-2 visa stamp for the passport and not the passport itself.
http://travel.state.gov/visa/temp/types/types_1265.html