Does time dilation tell us the distance to gamma-ray bursts?

Since the discovery that dim gamma-ray bursts last longer on average than bright ones (time dilation) the cosmological origin of this effect has been contested by various researchers. I discuss the current status of this issue and conclude that current models for a non-cosmological time dilation only explain part of the observed phenomenon, and even then betray themselves by distinct signatures in the data. As those signatures have not been seen, the cosmological origin remains the favoured explanation of the time dilation.