Low-ionization nuclear emission-line regions (LINERs), defined by the criteria [O II] lambda3727/[O III] lambda5007 greater-than-or-equal-to 1 and [O I] lambda6300/[O III] lambda5007 greater-than-or-equal-to 1/3, are generally thought to be related to classical active galactic nuclei powered by nonstellar continua. Based on the results of new photoionization models, however, we suggest that those genuine LINERs having weak [O I] lambda6300 emission (i.e., [O I]/Halpha less than or similar 1/6) may instead be powered by hot (T(eff) greater than or similar 45,000 K) main-sequence 0 stars irradiating solar-metallicity clouds of gas. The derived ionization parameter (U) is in the range 10(-3.7) to 10(-3.3), a factor of approximately 20 lower than in normal H II regions. Very high [N II]/Halpha ratios sometimes observed in LINERs may require a selective enhancement of nitrogen above the solar value. The presence of unusually hot stars (spectral type O3-O4) in such high-metallicity environments, together with low values of U, may be a natural consequence of the high gas densities, pressures, and masses in galactic nuclei. We also find that many weak-[O I] "LINERs" in the literature are not genuine LINERs, since they do not satisfy the [O I]/[O III] criterion; they were classified as LINERs only on the basis of their [O II]/[O III] or [N II] lambda6583/Halpha intensity ratios. These objects can easily be explained with our O-star photoionization models by increasing U up to approximately 10(-3).