I doubt that very much. it is true however that the manufactorer needs to perform the testing and paperwork or arrange to have it done, but final certification is still left to the associated authorities. You can can't just carry the CE mark without their audit of your results and approval.
You're right, the results are audited, but the testing is done by the manufacturer. By putting the CE mark on his product, he is certifying that it meets the specs. There are severe penalties for putting the mark on inadaquate products, but how he gets there is up to him.
But in the US, all the testing is done by the regulating agency. Documentation has to be provided on all materials and all maufacturing processes, even packaging. A big part of the testing is verification that the product EXACTLY matches the documentation, then that it EXACTLY meets all the performance specifications, including destructive testing. If the manufacturer changes thread suppliers, it is not the exact same product which received the approval, so it takes the full process on the new configuration. That's why the choices are so limited, and changes come so slowly.
