I would say that it would all go back to the specific contract. True customer specific requirements, such as EDI, labeling requirements, PPAP, Cpk's, etc., are always layed out in the contract. As I said, if they put ISO-14001 registration as a requirement in the contract, and we signed off on it, then go ahead and audit it.
Our customers send us general letters on a regular basis asking (demanding) certain things, but they aren't always part of the quality system. Your client should ask the registrar "how is achieving ISO-14001 going to affect the quality of my product?".
Of course, maybe that's how the Big 3 will start to implement their 'whims', put them under Customer Specific Requirements and force the auditors to issue a non-conformance. I can just hear the auditor now..."Well it seems that Ford recently issued a letter requesting that you provide defect-free product, at zero cost to them, for delivery yesterday. And based on what I can see, you didn't meet this Customer Specific Requirement, therefore, I have to write you up!".