You're correct if the car has the correct battery fitted which could in fact be part of the problem. If someone has previously changed the battery and not fitted an AGM battery, the stop-start will hammer the life out of a standard lead-acid and cause excess sulphation, drastically reducing the capacity of the battery.
However, if the battery is fully charged and not even the interior or hazard lights will work, it's pointing towards an earthing problem somewhere, rather than fuses.
That said, it could be a duff battery and an earthing problem..............