Registrars (or over here in the UK, "Certification Bodies", CBs) are either accredited or not, by an Accreditation Body (an AB).
In the UK our AB is UKAS; in the USA it's ANAB. They exist in over a hundred other countries, but not all.
The AB audits the Registrar (or CB) from time to time against, not ISO 9001, but ISO 17021. ISO 17021 says, essentially, that the registrar or CB must never get into the conflict of interest you describe. If the Registrar or CB continues to pass audits, they are "accredited" and the AB keeps a list of accredited registrars on its website.
Some registrars aren't accredited.
If your registrar is accredited you can complain about the conflict of interest to the AB. They will probably ask you to complain to the registrar first.
Well, that's how it's supposed to work. Mileage varies. Bare-faced conflict of interest like this though is very, very rare in my experience of the accredited audit world.
If your registrar is not accredited you're on your own.
Hope this helps,