I don't think I ever said AWS D1.1 speaks of certification. It speaks of welder performance qualification. And like I said previously, an employer can do their own qualification or accept certification, for instance, by a CWI or AWS Accredited Testing Facility in lieu of doing their own testing. As far as the code is concerned the manufacturer or contractor is responsible for qualification of welds. Certification is simply documentation of qualification to a particular standard.
ASME Section IX speaks of welding performance qualification. Again, it is the responsibility of the manufacturer or contractor.
Don't have a copy of API 1104 handy.
And yes, there are others who can certify welders besides CWIs. I never said otherwise.