It is okay to disagree with an auditor.
ABSOLUTELY. Auditors are human beings and sometimes they don’t understand the way you are doing things so you need to make them understand your processes.
Here is a great example I was auditing a company they had job descriptions and group training records but I wasn’t seeing how they showed an employee was competent in the job they were doing. After a while and several employees later, they told me there was a training matrix which showed the level of competency each employee was at in their positions. But because I did not ask to see ‘the training matrix’ no one was showing it to me. Sometimes an auditor does not speak the same language as you but if you have a good auditor, they should keep asking you questions to hopefully get the answer they need.
Looking for you to be compliant
An auditor is looking for you to be compliant to the standard, sometimes they are asking for certain things, they aren’t sure what you have named the document so it might take a while. Don’t get nervous just keep showing the auditor what documents you have.
Tell your auditor to go ahead and write a nonconformance report
If your auditor says they are going to write a nonconformance ask your auditor, what section of the standard will they be writing the nonconformance against? Take the time to read that section of the standard then look at your internal audits also previous audit reports and see what the auditors wrote under that section. This might help you see what documents were looked at under this section of the standard. Then show your auditor what previous auditors accepted.
If you show your auditor proof and the auditor stills writes the nonconformance ask your registrar what their appeal process is, this means you do not agree with the nonconformance. Once your registrar has all the evidence, they need they will make a determination if the nonconformance is legitimate or not. Most of the time the registrar will withdraw the nonconformance.