Richard A. Muller is a Professor in the Department of Physics at the University of California at Berkeley, and Faculty Senior Scientist at the Lawrence Berkeley Laboratory.
His course "Physics for Future Presidents" (at UC Berkley) has been released online. In the lecture about Radioactivity he says:
The US government has decided to make it illegal to make drinking alcohol out of oil.
Muller reiterates this in his books Physics and Technology for Future Presidents and The Instant Physicist:

The US government has decided that alcohol for human consumption must be made from "natural" materials, such as grains, grapes or fruit. That regulation rules out alcohol made from petroleum.
Natural alcohol gets its carbon from
plants; the plants got the carbon from
atmospheric carbon dioxide.
Atmospheric carbon dioxide is
radioactive because of the continued
bombardment of cosmic rays that
collide with nitrogen molecules and
turn it into C-14, radiocarbon.
Petroleum was also made from
atmospheric carbon, but it was buried
hundreds of millions of years ago,
isolated from the radioactive
atmoshphere. Radiocarbon has a
half-life of about 5700 years, and
after 100 million years, there is
nearly no atom of C-14 left.
So, a lack of radioactivity would be a giveaway that alcohol was not made from plant material.
Alcohol and Tobacco Tax and Trade Bureau - Code of Federal Regulations, Title 27, Chapter 1:
Spirits or distilled spirits:
The substance known as ethyl alcohol, ethanol, or spirits of wine in any form (including all dilutions and mixtures thereof, from whatever source or by whatever process produced), but not fuel alcohol unless specifically stated. The term does not include spirits produced from petroleum, natural gas, or coal.
This seems to confirm that drinking alcohol must not be made from petroleum.
And according to the Federal Trade Commission and the Department of Agriculture the standard method for measuring biobased content is ASTM D6866:

[ASTM D6866] applies to products with
carbon-based parts that can be combusted
completely into carbon dioxide,
and it uses radiocarbon, also known as
carbon 14, or 14C.
From ASTM International:
[ATSM D6866 are] standard test methods for determining the biobased content of solid, liquid and gaseous samples using radiocarbon analysis