Every construction/fabrication code or standard I have worked with provides acceptance criteria for the NDT methods specified. The acceptance criteria may be provided by the fabrication document by referencing a different standard, but never the less, it is provided.
In my humble opinion it should never be the inspector that makes the decision regarding establishing an acceptance criteria. Establishing acceptance criteria, i.e., establishing the size, length, nature, etc. of the discontinuity that is acceptable or rejected, is the engineer's responsibility. Generally the engineer is more knowledgeable about the magnitude of the stresses, the nature of the stresses, the influence of the discontinuity, mechanical properties of the materials of construction, operating environment, etc.than the inspector. Rarely does the inspector have that information, nor do most inspectors have the education or experience to use the information if it were provided.
There are those occasions where the item being tested does not fall under the auspices of an existing standard. In those cases the inspector may be requested to provide the engineer with some input, but the responsibility for establishing the acceptance criteria used for the inspection should remain with the engineer.
An inspector that makes up the acceptance criteria “on the fly” is someone that should viewed with suspicion and caution.
Best regards - Al