We reexamine critically the arguments raised against the theory that ultra-high-energy cosmic rays (UHECRs) observed at Earth are produced in gamma-ray bursts (GRBs). These include the limitations to the highest energy attainable by protons around the bursts' shocks, the spectral slope at the highest energies, the total energy released in nonthermal particles, and the occurrence of doublets and a triplet in the data reported by the Akeno Giant Air Shower Array (AGASA). We show that, to within the uncertainties in our current knowledge of GRBs, none of these objections is really fatal to the scenario. In particular, we show that the total energy budget of GRBs easily accounts for the energy injection rate necessary to account for UHECRs as observed at Earth. We also compute the expected particle spectrum at Earth, showing that it fits the HiRes and AGASA data to within statistical uncertainties. We consider the existence of multiplets in AGASA data. To this end, we present a Langevin-like treatment for the motion of a charged particle in the intergalactic-medium magnetic field, which allows us to estimate both the average and the rms time delay for particles of given energy; we discuss when particles of identical energies reach the Earth in bunches or spread over the rms time delay, showing that multiplets pose no problem for an explosive model for the sources of UHECRs. We compare our model with a scenario in which the particles are accelerated at internal shocks, underlining the differences and advantages of particle acceleration at external shocks.