This is less a photography question than a legal/business one, and the safest guidance is: get a lawyer to advise you for your jurisdiction.

Practically, printing services usually protect themselves through clear terms of service stating that the customer is responsible for ensuring they own the copyright or have permission to reproduce the image. Having that agreement in place is far better than assuming it is never your responsibility.

You generally can’t be expected to fully authenticate every claim or document, but it is sensible to do basic due diligence and reject suspicious jobs. If challenged, being able to show that you required customers to confirm rights and that you asked for documentation when something looked questionable is much better than having no process at all.

So: use lawyer-drafted terms, require customers to warrant they have the necessary rights, keep records, and decline orders that raise concerns.