I have the exact problem that you had . We are a machine shop that supplies medical implants and instruments to our customer's specifications. We do not label, package or sterilize sterilize our products. Yet our customer insists that, under the FDA definition, our products are considered "finished devices" - and therefore we are considered a "contract supplier" and are demandeing we register and list with the FDA. Who did you contact at the FDA? Or where can I find the type of exemption you describe clearly stated in the FDA regulation.
The distinction between Contract Manufacturing and "component making" is defined at 21CFR 807.65.
Your customer of course can demand anything they want, and you can agree to meet their demands or not. If you choose not to meet their demands, they can take their business elsewhere. Or, you can decide that their demands are unreasonable and tell them to go elsewhere. That's the nature of business relationships. As long as you do not distribute to end users, there is no FDA requirement that determines whether your status is Contract Manufacturer or Component Maker.
The core reason why your customer might want to be Registered and to List as a Contract Manufacturer is that they are Registered and List as a Specification Provider. They however can change their Listings to Manufacturer status, in which case it's perfectly fine for them to buy from a component maker.
Some companies and consultants apparently think that a Manufacturer must perform physical manufacturing in order to be have that status. My understanding is that that belief is incorrect. The process of turning a non-medical-device object, such as the product of a component maker, into a medical device is a
legal event. Who does what aspects of the
physical processing--the Manufacturer, a contract manufacturer and/or a component maker--is a secondary consideration.
Who did you contact at the FDA?
FDA DSMICA. 800-638-2041.