Of course it is! And the stated assumption is, like many, incorrect.
Certification has little to do with just producing 'required paperwork' (whatever that is). Certainly some documentation of processes, procedures and records is required. Indeed, organizations receive certificates when they need to perform corrective actions - nothing said a system had to be 'perfect'. It's in the nature of continuous improvement, after all....
Furthermore, unless an organization - having been audited and, perhaps with major system issues - cannot be certified even if they do pay for the audit up to that point. They will (normally) be required to submit actions and evidence of effectiveness, before a certificate is issued.
BTW - Americans have an expression regarding 'assumptions'. Do they have a similar one in your country?