If you can't doublespend, you have no chance of creating any fractional reserve. You can lend your "fake bitcoins", but that is useless to everyone else not part of your system.
I'd say we're not that far from such a situation. Many people already fall for "wrapped" Bitcoin, which it nothing more than a promise to real Bitcoin coming from a company hiding in the Cayman Islands. And yet, people fall for it.
Hence, why we still get emails from a Nigerian Prince, claiming to have my money!