New York magazine ran with a too-good-to-be-true tale Sunday featuring a teen who managed to score millions on the stock market before getting his high school diploma.

As has been widely reported, the story unraveled when The New York Observer published an interview with the teen, Mohammed Islam, in which he admitted the whole story had been a sham.

New York first appended an editor's note saying that although Islam denied making millions, the magazine had seen bank statements verifying his worth. Later, the magazine issued a full apology for the article, admitting the staff had been "duped."

But as of Thursday, the incorrect headline remains unchanged. Why?

"With the Editor’s note explaining that the story was false, we wanted to leave the story and headline intact for the record," wrote Lauren Starke, director of public relations for New York.

The magazine has amended the original headline to show that the $72 million was a rumored figure, but it didn't edit it to show that the premise of the story is inaccurate.

So should New York correct its headline? I asked Kelly McBride, Poynter's vice president of academic programs, and Poynter's Craig Silverman, founder of real-time rumor-tracking website, to weigh in.

McBride notes that the dynamics of online search complicate the question of whether to alter headlines. News organizations want to point out when a headline is misleading, but they also want the incorrect article to be recognizable under its original headline.

You want to make it clear that the story is no longer valid. But you don't want to change the headline in a way that the erroneous story with all its corrections starts coming up for people who are clearly looking for the right story.

So it's complicated. You have to make sure the audience knows immediately by looking at the page, or even at the search results on Google, that this information was corrected. But you don't want to make it seem like you had it right all along.

While he understands the concern for transparency, Silverman warns that readers might not read past the erroneous headline to find the truth, especially if it's automatically included in a tweet or Facebook post.

Research has shown that readers retain headlines more than body text. The headline is also what is automatically loaded into a tweet or Facebook post if people click on a sharing button. While I appreciate the idea that they do not want to scrub away the original mistake, the issue here is that they are compounding the damage by creating cognitive dissonance for anyone who reads the headline and then the editor's note.

I would also point out that the editor's note itself also focuses on the $72 million claim. It is possible that someone who reads the headline and then reads the note comes away thinking that maybe the kid did make some money. And what about the claim that he's opening his own hedge fund when he turns 18? That isn't addressed in the editor's note, and yet it's in the headline. Is it true?

People need to know when they come to the page that this article has been significantly changed, and this must be flagged in the headline. They could then include the original headline text in the Editor's Note in order to reinforce the change and retain the original.