Most American Style refrigerators typically have an annual load of around 500-600 kWhrs/year for the A and A+ rated European market. So I would estimate around 2kWhrs/day worst case. So 18-24 hrs would be about right. But then again the refrigerator might be an older inefficient model where it could easily be 3-4kWhrs/day so 9-12hrs might be a typical run time using the batteries especially if the inverter is a low efficiency model i.e 50% even when used with a modern refrigerator design.

Is the 3 hrs quoted an empirical or experimental test?