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We report a degeneracy between the gravitational-wave signals from quasi-circular precessing black-hole mergers and those from extremely eccentric mergers, namely head-on collisions. Performing model selection on numerically simulated signals of head-on collisions using models for quasi-circular binaries we find that, for signal-to-noise ratios of 15 and 25, typical of Advanced LIGO observations, head-on mergers with respective total masses of $M\in (125,300)M_\odot$ and $M\in (200,440)M_\odot$ would be identified as precessing quasi-circular intermediate-mass black hole binaries, located at a much larger distance. Ruling out the head-on scenario would require to perform model selection using currently nonexistent waveform models for head-on collisions, together with the application of astrophysically motivated priors on the (rare) occurrence of those events. We show that in situations where standard parameter inference of compact binaries may report component masses inside (outside) the pair-instability supernova gap, the true object may be a head-on merger with masses outside (inside) this gap. We briefly discuss the potential implications of these findings for the recent gravitational-wave detection GW190521, which we analyse in detail in [Phys. Rev. Lett. 126, 081101].