The difference is who Ray needs to inform of the discrepancy and how to get it corrected. If he works for the contractor he will have to address the issue with the person that is responsible for developing the WPS and the supporting PQR(s) and upper management if he isn't satisfied with what is going on. If he is a third party inspector, he has to go to the "owner" so the problem can be handled through the proper channels. It isn't the CWI that has the authority to approve or disprove the welding documentation, that lies with the Engineer per AWS D1.1. The authority given to the CWI by the code is very limited. He observes and reports his findings in most instances and any communication should be handled through the Engineer.
Lincoln's product literature says the 960 is a neutral flux that is compatible with the L61 filler metal. The combination is recommended for mild steel. That brings up the question: what is the alloy being welded? The combination meets the F7A2-EM12K-H8 AWS classification. It produces a tensile strength of 75 ksi, yield strength of 61 ksi, elongation of 32%. I assume the data is for all weld metal. Ray might want to check the Lincoln label on the box to see if the FM is classified under more than one AWS/ASME classification. I've encountered this on more than one occasion, i.e., filler metal used with GMAW is classified as such, but also classified as SAW filler metal. So, check the box label if it hasn't already been done.
If the existing welding being performed is acceptable or not depends on the applicable code, if any. If AWS D1.1 is applicable, it is the Engineer's responsibility to address the situation once the CWI makes his concerns known. The alternatives available to the Engineer are to rewrite/revise the WPS (and qualify the procedure if necessary) or require Production to follow the existing WPS.
I would also ask, "Where is QA/QC?". They have a roll to play in this scenario. Perhaps the CWI, Ray, in this case is "QA/QC", in which case the situation must be also bought to the attention of "management, i.e. the owner if this is a small operation.
A little homework on Ray's part in preparation of going to management is well advised. Make sure he has all the information needed to substantiate his position.
There is little additional advice to be offered without knowing all the details of the WPS and what is being welded to what requirements, i.e., what edition of the code, base metal specification, joint details, whether CVN is a requirements, what is the application, etc. Having bits and pieces of information simply leads everyone down a country road without a map.
Best regards - Al