I was having an issue having enough hides so I turned off storing books in the markets and storehouses. I wanted books only for my libraries. The UI says the book binder can hold 10 but it never seems to hold more than 1 and always spams messages about out of storage (for books). Shouldn’t the warning only come up when the book binder is full?
We verified that book binder does in fact store up to 10 books. We could not repro a “storage is full” warning on the book binder with less than that.
Since books are produced slowly, you’re likely seeing villagers grabbing books as soon as they are produced to use in their shelters.
All I can say is I had to turn off the notification as it kept firing again and again showing I had 1 book in storage and verified that one book was in the book binder. 
Was it a notification about no places to store it? That would make sense. Production buildings do not count as storage and if there is nowhere to put produced goods, you would get that warning.
Yes, the kind that is shown on the upper central portion of the screen with a magnifying glass that opens the resources screen, showing books outlined in red. I guess I will just nuke the book binder and raze the libraries as there is not enough benefit and books seem to disappear quicker than fruit rotting.