[ghufran_syed]

I think the weakness here is in the first step "Collects identifying documents". If a potential terrorist in some countries can procure 'official' documents with a different name than their own, then all the rest of the screening will fail, because they will be checking the record of a presumably innocent resident of that country, while the person who would actually enter the country if approved would be someone else. Ideally, the government doing the checking also needs to be able to get or verify additional information from the potential refugee's home governments.

It therefore seems reasonable to me you might want to restrict travel from countries that either have such weak governments that fake 'official' documents can be obtained (somalia, syria, yemen etc) or countries that have a stated policy of non-cooperation with the US government on such matters (Iran).

That would also explain why you would not exclude people from 46 other muslim majority countries - there would be no reason to if their official documents can be relied on, and they are responsive to queries from the US when some information needs to be verified.