I thought Archimedes solved this problem 2500 years ago.
A properly weighted gold/tungsten/lead bar would pass the Archimedes test...
It would not pass hydrostatic specific gravity measurement
Also people have wondered if Archimedes was capable of measuring the differences in water volumes precisely enough.
An object denser than water will only displace its volume, so it would not matter if this was lead, copper, quartz, or gold. They all would displace the same amount of liquid given it has the same dimensions.