"Um, sorry, that is incoherent. The wireless network is either configured for open access, or it requires a key."
Um... sorry but THAT is silly. By your definition, anything that isn't nailed down is free for the taking. My gas grill isn't welded to the porch and the cover isn't locked, but you don't have permission to use it. The same is true for my wireless network, whether it is open or requires a key. I pay for the service, so the service belongs to me.
Try this model instead: If somebody else paid for it, it isn't yours unless and until they give you permission to use it.
When I was young, we didn't have to lock our doors and most people left their keys in their cars. Your attitude put an end to those times.
You misunderstand. Permission IS requested AND granted. It's as if there's a sign on your gas grill saying "yes, you may use this" - and your grill is sitting on the public sidewalk. The router configurably broadcasts its availability - that's an offer of service, which can trivially be shut off.
Additionally, the wireless network at the library in question IS set up SPECIFICALLY for public use.
It is also common practice (unlike with gas grills) to leave wireless networks open for public access. Mine is open.
Again, the router is broadcasting. You're not leaving your keys in your car - you're actively placing them in my house on my living room table. There's a difference between an unlocked door and a herald shouting "Come on in!" which is essentially what a router does.
It is not a physical object that you have to lock up or people can walk off with it. If is only open if you deliberately configure it to be.