Fake besties is a term used in New Zealand, it means when two people are very close but don't like to stereotype themselves as being best friends or don't personally believe they are best friends so instead they call each other "Fake Besties"
Logan: Sarah and Emma you two always hang out, are you guys besties?
Sarah: NO! We're fake besties
Logan: Fake Besties?
Emma: We are fake besties because we are not actually besties but are tight as and talk lots!