The simplest and arguably the most ubiquitous pattern in seed dispersal mutualisms is size coupling: large frugivores tend to consume larger fruits and small frugivores tend to consume smaller fruits. Despite the simplicity of this pattern, the potential mechanisms responsible for fruit–frugivore size coupling are mechanistically divergent and poorly resolved. Size coupling could arise deterministically, if large frugivores actively seek out larger fruits to maximize their foraging efficiency. Alternatively, size coupling could also arise passively, if frugivores forage randomly, but are able to consume only those fruit species that are smaller than their gape width. I observed birds forage for fruits in a New Zealand forest reserve at approximately five‐day intervals for six years to test for fruit–frugivore size coupling. I then derived a suite of network analyses to establish whether fruit–frugivore size coupling was best explained by active or passive foraging by frugivores. Results showed a strikingly strong pattern in size coupling; the average size of fruits consumed by each frugivore species increased with their maximum gape width. Simulation analyses revealed that over 70% of variation in interaction frequencies in the observed fruit–frugivore web could be explained by a size‐constrained, passive, foraging model. Foraging models in which birds foraged actively for different‐sized fruits to improve their foraging efficiency performed more poorly. Results were therefore consistent with the hypothesis that apparently nonrandom patterns in seed dispersal mutualisms can sometimes arise from simple stochastic processes.