I just received an email from OverDrive:
This message is to inform you that some Kindle users may be prompted to 'Buy now with 1-Click' when attempting to download a Kindle book from your OverDrive-powered website, rather than being taken to a page to redeem their checked out eBook title. Unless the user wants to buy the title, they should not click this option.
We are working to resolve this issue as quickly as possible, and will send an update when we have further information.
In the meantime, a message will be posted at your OverDrive-powered website to alert Kindle users.
OverDrive's Library Partner Services