How do ebook libraries work? When you think about them in the same way as a traditional library, with physical books, things get complicated quickly. If you send an ebook to a patron's device, how do you make sure they eventually delete it? How do you ensure the devices people use obey the library rules and don't allow copying? Instead, you need to think about access, not possession.
The library itself is a collection, akin to an Amazon user account. And when you're talking about accessing their collection, you either need to think of devices or linked accounts. The digital library can function perfectly well if they have a collection of Kindles they can physically lend out, as long as those Kindles can't buy anything on library credit. Alternatively, since the Kindle is supposed to be controlled via DRM, you can just allow any patron to link their account to a public library and gain access to any books contained there, on any device that supports the Kindle software. If they are unlinked from the library, they lose access to those books.
Mokalus of Borg
PS - If your DRM is as good as you say it is, this should be easy.
PPS - I'm pretty sure they wouldn't allow this, "for security reasons".