Found a mistake in a proof about when GGH will decrypt incorrectly
Okay, this was a really stupid mistake by me. I got confused because some sources use notation where $R$ and $B$ have the basis vectors as rows. However Goldreich, Goldwasser and Halevi have the basis vectors as columns so 
$$B=RU\implies U=R^{-1}B.$$ Hence the matrix is unimodular and the proof works. Sorry about the inconvience.