On my recent CB cruise this past summer, housekeeping/maintenance could not get our refrigerator to work properly...at all, over 13 days. We were informed that it was a cooler and not a refrigerator (barely would cool anything). We were also told there was none on the ship to replace it and that it was a specific size and could not be replaced either.
On a cruise to Hawaii on the Grand, I would "store" chocolate covered strawberries in the refrigerator. They would mold within days. That "cooler" never felt cold either.
That has been my experience. Don't know if it is because these were older ships. I will only use the box to store things overnight. Anything else, I would not deem safe like I would at home.