Why auditors copy documents from one organization to another? Is it to make their jobs faster or to use it as a start point in for the new organization? Though it was stated in the training that copying documents is not a good practice.
From your question is not clear whether the question is about audit documents (e.g., audit plans, audit checklists, etc.) or auditee documents, so this answer will cover both alternatives.
For audit documents the auditors have their own templates which they use as they see fit.
Regarding auditee documents, document copy for non-audit purposes is strictly forbidden (very often documents are copied and sent to the auditor when a remote audit is performed), because the document does not belong to the audit area, and when the audit is performed on other organization, in general there is a confidentiality agreement signed with the customer.