Final answer:
The television star must prove that the magazine either knew the story was false or that it acted with reckless disregard of the truth, which is a high standard of proof and requires showing actual malice or a significant level of fault.
Step-by-step explanation:
If the famous television star decides to sue the magazine for publishing incorrect information, she will need to demonstrate that the magazine acted with a significant level of fault in publishing the falsehoods.
Since the individual in question is a public figure, according to established legal precedents such as New York Times v. Sullivan and Curtis Publishing Co. v. Butts, she must show that the magazine either knew the story was false or acted with reckless disregard of the facts.
This standard is relatively high and requires proving that the magazine had a subjective awareness of the falseness of the claim or exhibited a high degree of awareness of probable falsehood.
More specifically, the actress does not necessarily have to demonstrate that the magazine has a history of being negligent with facts nor that the magazine failed to contact her before publishing the story, though these elements could potentially strengthen her case.
It would also be supportive of her claim to demonstrate that the magazine had the opportunity to discover the story was false and did not take it, which could be seen as a form of recklessness.
Ultimately, the burden lies on the public figure to establish that the publication contained defamatory falsehood made with actual malice or reckless disregard for the truth.