They propose that every instance of a specific codon in the DNA is mutated and replaced by another codon. Although this doesn't seem like a large amount of the genome, it is the specificity of replacement that makes this mechanism statistically impossible. This is certainly an overestimate and doesn't at all appreciate the tremendous changes in codon usage in many genomes such that many codons are essentially unused in some organelles. I won't try to explain the proposed mechanisms for tRNA changes off the top of my head but will try find the papers tomorrow. I am sure that there are others though that are probably more familiar with the odd cases and can illuminate you on this topic.
Genomic evolution drives the evolution of the translation system.
Biochem Cell Biol. I am now shamelessly promoting myself on the web.