Giudici and Hart have observed that the proof of Theorem 3 is not correct 
as stated, as it does not allow for the possibility that g^2 is in S. 
Otherwise put, Theorem 3 as stated only applies to the modified
notion of product-free subsets, where you consider products of 
distinct pairs of elements of the subset.

The paper of Giudici and Hart does not appear to be published.
It can be found online at

http://eprints.bbk.ac.uk/archive/00000439/01/SmallCFSF5.pdf