To (hopefully quickly) clarify the deal, if the book isn't copyrighted, then the book is in the public domain, no question.
However...if the book is derived (directly, I mean, like outright copying or adaptation) from a copyrighted work, then the original author would have grounds to prevent distribution. It also couldn't be used by anybody for adaptation, since it'd be adapting the ORIGINAL material.
As I interpret things, it's sort of like an anthology. Individual elements (stories, specifically) may have individual copyrights, even though the collection is in the public domain, and that single copyright can't be violated just because someone other than the owner messed up. But in this case, we don't know what those copyrights might be to research them.
(That's not to say "no," just showing where the complexity is. Other thoughts, as always, would be appreciated.)