I think it is a hoax. In the whole conversation I don't think the sister is referred to by name. If you were talking about your sister, or your SO's sister, wouldn't you use her name? Unless of course you know you have 1000s of strangers listening on the radio, and want to be sure they follow the conversation.
Good point... I never refer to my partner's sister as "your sister", because she has a name and stuff.