Why should it seem strange? If you own stock I can lend it and sell it outright, and as long as I buy it back and provide it to you at the exit of the deal everything fine.
If you own a book and I buy it but under a deal that defines you should keep it locked up in a safe. I still own it and have the right to lend it out digitally under CDL, yet it's physically with you. Why is it strange to forgo that madness and just let me provide digital lending services on your behalf? I mean just because it's my lending system doesn't mean I should need to own everything that's being lend out. Amazon doesn't have to own everything they sell.