I think it is because the fire was burning very hot "HollyWOOD" :-)
Alternatively, perhaps the gold was cheapened by adding lead (or silver/some other alloy such as in the Archimedes story). Lead was often used, make objects feel heavy like true gold and be gold coated but were cheaper to make.
Why this might have worked here:
Gold melts at ~1948F.
Lead melts at ~621F.
Wood goes through several stages before burning. As temperature increases, moisture boils off. At 450 degrees F, wood particles form volatiles, which produce the flames we see. At 750 degrees F combustion becomes possible. An oak log needs between 200 and 400 degrees to maintain combustion and burns at a maximum of 900 to 1100 degrees.
Hence an average cookfire (say a good boy scout campfire) can get to an average of 900-1000. Easy enough to melt lead. If it has an extremely good bed of coals and the right pitch to get a good draft going, you might get to 1200 or so. But, you would still be several hundred degrees Farenheit short of melting pure gold. Even silver takes ~1700 which would be really pushing it on a regular cookfire.
More likely it is because the t.v. producers simply took the story as originally written back in 1996 and never bothered to fact checked the author's claim to see if it would work. I remember reading this scene back in Asimov's when it first came out. I remember thinking at the time it was hogwash and I haven't changed my mind. However, it is still a brutal image.