She could, and perhaps should, take legal action if she is slandered or libelled.
Her problem with attempting that is that she hasn't been slandered or libelled.
She lied, repeatedly. That can very easily be demonstrated to any Court. Exhibit A might be this:
It is abundantly clear that she was the spider at the centre of a web of deceit which caused countless major newspapers to publish rubbish about her flying solo from Africa; and to Oz; and across the USA. Any barrister worth his or her salt could bring a hundredweight of broadsheet and tabloid headlines to Court to show how all-encompassing the cheatery was.