In this paper, we investigate the physical associations between blended far-infrared (FIR)-emitting galaxies, in order to identify the level of line-of-sight projection contamination in the single-dish Herschel data. Building on previous work, and as part of the Herschel Extragalactic Legacy Project, we identify a sample of galaxies in the COSMOS field, which are found to be both FIR-bright (typically ˜15 mJy) and blended within the Herschel 250-μ m beam. We identify a spectroscopic or photometric redshift for each FIR-bright source. We conduct a joint probability distribution analysis on the redshift probability density functions to determine the fraction of the FIR sources with multiple FIR-bright counterparts that are likely to be found at consistent (Δz <0.01) redshifts. We find that only three (0.4 per cent) of the pair permutations between counterparts are >50 per cent likely to be at consistent redshifts. A majority of counterparts (72 per cent) have no overlap in their redshift probability distributions whatsoever. This is in good agreement with the results of recent simulations, which indicate that single-dish observations of the FIR sky should be strongly contaminated by line-of-sight projection effects. We conclude that for our sample of 3.6- and 24-μ m selected, FIR-bright objects in the COSMOS field, the overwhelming majority of multicomponent FIR systems are line-of-sight projections within the 18.1-arcsec Herschel beam, rather than physical associations.