Owners that understand what they are up against usually modify the acceptance criteria of the ASME construction code in the project specifications.
As an example: Section VIII of the B&PV code does not include a specific requirement for undercut. They have a limitation for "base metal thinning due to the manufacturing process", so to clarify many owners add criteria for undercut and they include a definition of the condition.
Another example that comes to mind is the allowable undercut per B31.1 for Power Piping. The standard is 1/32 inch regardless of the pipe wall thickness. One of our projects utilized 0.035 inch wall tubing. The owner modified the criteria to no more than 10% of the wall thickness, but not to exceed 1/32 inch.
Check the project specifications to see if the owner/engineer modified the code requirements. They can be more stringent than the code, they just can't be less stringent than the code.
Best regards - Al