No way! If you include a copy of your quality policy in your manual, and your manual is approved, then that makes your quality policy approved. If you can show that you review the quality policy periodically (management reviews) then that makes your quality policy approved. Man, I think that audits by customers are the worst! Somebody tells them something about what to look for, and they just can't see anything else. (Did they come in with their checklist already filled out like my NQA-1 customer's audit did?)
Sure, a signed policy hanging somewhere (appears) to show commitment. I can sign stuff all day long, and either intend or not intend to follow through with it. My first ISO system I worked on, the employees all got together and decided that THEY should sign the quality policy, because THEY were the ones that were going to be doing the work and ensuring product conformance. It was a great way for them to be a part of the system. The second one, managers signed. The third one, nobody signed. I've decided that the longer you are in the business, the more realistic you become. You know that it isn't a signature on a piece of paper, but a culture.
Tell them you can show that it is approved, and get on with your business. After all, it is your business, not theirs. If you perform every nit-pickin' task that every customer brings to you, you'll not be able to supply them product. My boss once used that on an especially outrageously demanding auditor. Called his boss, and said, "we can fix this nonconformance cited, even though there is not one shred of evidence that it is truly a nonconformance, or we can produce you product and get it shipped to you on time. Which do you want, we cannot do both?"