This. Rest is a shared responsibility between the company and you. The FAA will not look kindly on a claim of ignorance or trying to put the blame back on the company should there be an issue. It's also not just if fatigue is involved. If anything happens and they look into the conditions leading up to the incident, illegal rest could easy come to light.

The original question focused on the 13 days per quarter, but it sounds like they are not complying with 10 hours of rest in the previous 24 either. That to me is the bigger safety issue on a day to day basis.

Unfortunately the definitions of rest are not clearly defined in the regs. You have to find it in the FAA Legal Interpretations. Sadly many people do not know about these documents and how they affect what they do. Before any sort of confrontation with your boss I'd suggest educating yourself on what they say. Google FAA Legal Interpretation, go to the FAA website and put in "Rest" into the search. You could read for days.