The Late Heavy Bombardment (LHB), a hypothesized impact spike at ̃3.9 Ga, is one of the major scientific concepts to emerge from Apollo-era lunar exploration. A significant portion of the evidence for the existence of the LHB comes from histograms of 40Ar/39Ar “plateau” ages (i.e., regions selected on the basis of apparent isochroneity). However, due to lunar magmatism and overprinting from subsequent impact events, virtually all Apollo-era samples show evidence for 40Ar/39Ar age spectrum disturbances, leaving open the possibility that partial 40Ar* resetting could bias interpretation of bombardment histories due to plateaus yielding misleadingly young ages. We examine this possibility through a physical model of 40Ar* diffusion in Apollo samples and test the uniqueness of the impact histories obtained by inverting plateau age histograms. Our results show that plateau histograms tend to yield age peaks, even in those cases where the input impact curve did not contain such a spike, in part due to the episodic nature of lunar crust or parent body formation. Restated, monotonically declining impact histories yield apparent age peaks that could be misinterpreted as LHB-type events. We further conclude that the assignment of apparent 40Ar/39Ar plateau ages bears an undesirably high degree of subjectivity. When compounded by inappropriate interpretations of histograms constructed from plateau ages, interpretation of apparent, but illusory, impact spikes is likely.