It has been suggested that radiative transfer effects may explain the unusually high equivalent widths (EWs) of the Lyα line, observed occasionally from starburst galaxies, especially at high redshifts. If the dust is locked up inside high-density clouds dispersed in an empty intercloud medium, the Lyα photons could scatter off of the surfaces of the clouds, effectively having their journey confined to the dustless medium. The continuum radiation, on the other hand, does not scatter, and would thus be subject to absorption inside the clouds. This scenario is routinely invoked when Lyα EWs higher than what is expected theoretically are observed, although the ideal conditions under which the results are derived usually are not considered. Here we systematically examine the relevant physical parameters in this idealized framework, testing whether any astrophysically realistic scenarios may lead to such an effect. It is found that although clumpiness indeed facilitates the escape of Lyα, it is highly unlikely that any real interstellar media should result in a preferential escape of Lyα over continuum radiation. Other possible causes are discussed, and it is concluded that the observed high EWs are more likely to be caused by cooling radiation from cold accretion and/or anisotropic escape of the Lyα radiation.