S. Lee (2006) proposes that bare NPs without Acc markers are more restricted or "marked" from the perspective of neo-Gricean pragmatics, utilizing Levinson's (2000) pragmatic Case, on the other hand, gives rise to "hard" semantic/pragmatic effects such as specificity, definiteness, D-Linking, and the like.
long.time-at M.-Nom a/a.certain man-(Acc) meet-Past-Dec '(Long time ago) Mary met a man.'