It has been proposed that patterns in the usage of synonymous codons provide evidence that individual tRNA molecules are recycled through the ribosome, translating several occurrences of the same amino acid before diffusing away. The claimed evidence is based on counting the frequency with which pairs of synonymous codons are used at nearby occurrences of the same amino acid, as compared to the frequency expected if each codon were chosen independently from a single genome-wide distribution. We show that such statistics simply measure variation in codon preferences across a genome. As a negative control on the potential contribution of pressure to exploit tRNA recycling on these signals, we examine correlations in the usage of codons that encode different amino acids. We find that these controls are statistically as strong as the claimed evidence and conclude that there is no informatic evidence that tRNA recycling is a force shaping codon usage.