The librarian only gives you permission to loot the library shelves (they change from red to white after you talk to her), not the books that are just lying around. You'd have to use invisibility or sneaking to get those.
She does, but it appears to have skipped the Rat Extermination book (which might have been added late in development as hint to an endgame quest). Which would be a bug...
Picking it up still gives it to you anyway, but with an attitude penalty (if seen).
