The origin and configuration of the gas that emits broad lines in Type I active galactic nuclei is not established yet. The lack of small-scale structure in the broad emission-line profiles is consistent with either a smooth gas flow or a clumped flow with many small clouds. An attractive possibility for the origin of many small clouds is the atmospheres of bloated stars, an origin that also provides a natural mechanism for the cloud confinement. Earlier studies of the broad-line profiles have already put strong lower limits on the minimum number of such stars, but these limits are sensitive to the assumed width of the lines produced by each cloud. Here we revisit this problem using high-resolution Keck spectra of the H? line in NGC?4395, which has the smallest known broad-line region (~1014?cm). Only a handful of the required bloated stars (each having r* ? 1014?cm) could fit into the broad-line region of NGC?4395, yet the observed smoothness of the H? line implies a lower limit of ~104-105 on the number of discrete clouds. This conclusively rules out the bloated-stars scenario, regardless of any plausible line-broadening mechanisms. The upper limit on the size of the clouds is ~1012?cm, which is comparable to the size implied by photoionization models. This strongly suggests that gas in the broad-line region is structured as a smooth rather than a clumped flow, most likely in a rotationally dominated thick disklike configuration. However, it remains to be clarified why such a smooth, gravity-dominated flow generates double-peaked emission lines only in a small fraction of active galactic nuclei.