We utilize high-resolution (R~60,000), high S/N (~100) spectroscopy of 17 cool Pleiades dwarfs to examine the confounding star-to-star scatter in the 6707 Li I line strengths in this young cluster. Our Pleiads, selected for their small projected rotational velocity and modest chromospheric emission, evince substantial scatter in the linestrengths of 6707 Li I feature that is absent in the 7699 K I resonance line. The Li I scatter is not correlated with that in the high-excitation 7774 O I feature, and the magnitude of the former is greater than the latter despite the larger temperature sensitivity of the O I feature. These results suggest that systematic errors in linestrength measurements due to blending, color (or color-based T_eff) errors, or line formation effects related to an overlying chromosphere are not the principal source of Li I scatter in our stars. There do exist analytic spot models that can produce the observed Li scatter without introducing scatter in the K I line strengths or the color-magnitude diagram. However, these models predict factor of >3 differences in abundances derived from the subordinate 6104 and resonance 6707 Li I features; we find no difference in the abundances determined from these two features. These analytic spot models also predict CN line strengths significantly larger than we observe in our spectra. The simplest explanation of the Li, K, CN, and photometric data is that there must be a real abundance component to the Pleiades Li dispersion. We suggest that this real abundance component is the manifestation of relic differences in erstwhile pre-main-sequence Li burning caused by effects of surface activity on stellar structure. We discuss observational predictions of these effects.