Shane;
ASME Section IX provides exactly the same latitude to all other ASME code sections, i.e., B31.1, B31.3, Section VIII, etc., in fact, you will see a statement in the front matter of all ASME codes that says the code does not take the place of sound engineering judgment.
In my opinion, where the code states "the Engineer (OEM) can add to, delete from, or otherwise modify, the requirements of this code to meet the particular requirements of a specific structure" it is simply placing responsibility on the OEM for the actions they take.
We have to remember that the code is largely an engineering guide to "good practices" and if the engineer decides to take some exception to it then they should be able to justify their actions should an event occur which places them in a situation of litigation.
Get the deviation in writing is my advice. Best of luck!
I would say this OEM is committing gross negligence by using radiography to examine GMAW-S welds, since this process is known to produce tight lack-of-fusion defects and radiography is known to be not reliable for detecting these defects. This is a bad engineering decision.