The Owner is legally responsible for determining which code section is applicable under the auspices of ASME B&PC Code. The construction code, i.e., the code section such as Section I, Section VIII, B31.1, B31.3, etc. references Section IX for qualifying the welder and the procedures.
The construction code can modify the requirements of Section IX. For instance, if you are working to B31.3 and the pipe system is declared to be "high pressure", performance tests must be evaluated using a guided bend test, i.e., RT is not acceptable.
In the absence of a modification by the construction code, qualification and evaluation of the test samples is per Section IX. In the case of performance qualification, Section IX offers a couple of alternatives, i.e., RT of the test coupon, RT of the first production weld, or guided bend tests may be used.
The customer, i.e., the Owner, usually represented by an engineering firm can impose any requirements they feel are appropriate provided they do so in the RFQ, purchase order, and the project specifications. If the Owner feels that RT provides greater assurance the test coupons will be properly evaluated, it is his prerogative to add that requirement to the project specification. In the absence of listing the requirement in the project specification, the Owner cannot unilaterally impose such restrictions or requirements.
That being said, after witnessing several performance tests at a mechanical contractor's facility, I understand the Owner's concerns. In my case, I was testing a welder to AWS requirements. I was witnessing the welding of the Fillet Break Test coupons and performing the break test at the contractor's facility. While doing my work the contractor was qualifying several welders on pipe. For that purpose all the test witnessing and evaluations were performed by the shop foreman, i.e., no third party was involved. The shop foreman would cut the coupons for bend testing. He would then perform the guided bend test and if any open defects were observed on the convex surface, remove the defect by grinding and then pronounce the test as "Passed". It was little wonder that very few people (omission of the term "welder" is intentional) failed the open root pipe tests.
Best regards - Al