Qantas? How about the B744 overrun on landing in BKK during a TS? Major pilot error. The aircraft should have been written off but was repaired at great expense in order to maintain the "no hull loss" statistic. A company that until very recently was relatively small and flew exclusively medium- and longhaul in sunny weather conditions should be very careful about boasting over a "safety" record.
Compare Qantas to large airlines operating short haul in winter conditions and this safety boast shines a little less brightly.
Scratch the surface of this company and a few major screw ups come to light.