So I understand....
They are manufacturing a product for you, where they are creating a hole in something. They are using device A to measure the inside diameter of that hole. Let's say they measure 1.0 inch
They then take device B to measure device A in the same position where it measured device A. Device B then yields 1.0 inch. They then accept the values given by device B for product acceptance.
If that is accurate,
1. That seems like an odd way to go from point A to point B. I don't understand why they have such a convoluted process.
2. More importantly, have they done any kind of gauge analysis/ uncertainty estimation of how good this process is? It sounds to me like there is quite a bit of error in that. Have they had a lot of failures?
3. Umm... last time I checked, you're the customer. I find it sad customer service on their part that they don't at least listen to the customer better and possibly see if there is a better way of doing their measurements.
They have the responsibility to not only assure their processes are "compliant" but more importantly, that they are satisfying the customer. I know that sounds hokey; but to me, is important. They need to win your confidence that they are producing quality product for you. If they want your long term business, they need to go the extra mile for that. Otherwise, it's worth your time and effort to search for other potential vendors, IMO.