More seriously, it could very well be an entirely different business, and she just liked the name Style Club. Re-using almost the same business name is hardly a crime.
The biggest issue, in my opinion, is that she "shut down" her old business without notifying her investors. Now, to be practical, most customer-less startups (that is, most startups) don't have an official day where everyone walks away. One founder gets a day job, another starts spending a little more time on other projects, and so on. Everyone involved, including investors, knows that its dead. Startups that haven't done anything for 4 years don't suddenly take the world by storm.
Nevertheless, she should have "officially" shut down her startup if she was going to go on national TV pitching her new one.
While she handled this poorly, I would be wary of placing too many restrictions on allowing entrepreneurs to start new businesses. Although if they are nearly identical and you are a success, you will get into trouble (just ask Zuckerberg...)