Unless I had a third party drill out and sample the bar, I would be suspicious.
Drilling gold is invasive. I wonder if there is reliable, accurate, and non-invasive method to determine whether something is gold or tungsten.
Tungsten has an atomic weight of 183.84, Gold is 196.97 so displacement in water of gold would be less than that of tungsten for equal weights.
A non-invasive method to very accurately measure density to correlate with atomic would be very useful. Of course, one would also have to compensate for alloys with small amounts of copper, as most gold coins contain some copper for hardening. I would think that if SHTF, such a device would be useful especially as the gold price would rise in a crisis along with counterfeiting.