  Very recently, the Pierre Auger Collaboration reported a $4.5\sigma$
correlation between the arrival directions of the highest energy cosmic rays
and nearby starburst galaxies. The cosmic rays producing the anisotropy signal
have been proposed to originate in low-luminosity gamma-ray bursts (llGRBs). On
the basis of the well-justified assumption that at redshift $z<0.3$ the host
metallicity is a good indicator of the llGRB production rate, we show that the
association of llGRBs and the starbursts correlating with Auger data is
excluded at the 90% confidence level.
