There is a "collective works" copyright, so I guess -- I am also not a lawyer -- that if one made a copy of some database, it may be infringing on the creator's rights even if the contents of the database consisted solely of public domain works.
>You are free to copy and use individual images but copying and distributing the complete collection may infringe what is known as the “collective works” copyright. Collections of public domain material will be protected if the person who created it has used creativity in the choices and organization of the public domain material. This usually involves some unique selection process, for example, a poetry scholar compiling a book -- The Greatest Poems of e.e. cummings.
I don't think JSTOR is using what could be described as a unique selection process.
We've discussed this on HN before. Reproductions of public domain works are not protected by copyright.
Edit: Of course a significant portion of JSTOR's archive does consist of copyrighted works.