Obviously, yes, if you actively refuse to provide documentation, that fact could be used to the advantage of the other side. “We asked for proof that he received the payment but he refused to provide his accounting records.”
Presumably the only point where it would be advantageous is if lack of documents makes it impossible to prove perjury. But then, if perjury is a real possibility it becomes a criminal case and the police can kick in your door looking for the documents. (with a warrant, of course).
What about third parties in civil cases? Can the court (at request of one side?) demand a third party produce documentation that could relate to a case? (I.e. can the other side demand the bank produce account statements?)
The third party can refuse by asserting its own privilege arguments. They are also (sometimes) permitted in state actions to request reasonable costs associated with the document production. For some bizarre reason, this rule doesn’t seem to be true in federal practice. But my experience is not in civil law, and definitely not in federal civil litigation, so I’ll defer further snark in favor of someone who actually knows of whence he speaks.