NEW YORK (TheStreet) -- Over a billion people use Facebook's  (FB)  site on a daily basis. So when reports surfaced of fake news stories on the site, it made headlines.

While some have called for the social media giant to take a bigger role in policing the information posted on its site, Jessicea Lessin, editor-in-chief of The Information, isn't buying it.

In a New York Times op-ed piece she wrote, "I simply don't trust Facebook, or any one company, with the responsibility for determining what is true."

She told CNBC Tuesday that misinformation on Facebook "is a huge problem. I was frankly pretty shocked at how many commentators have reached the conclusion that the answer is Facebook hiring journalists, and editors and fact checking.'

Allowing the public to believe Facebook is fact checking the information on its site could be "very dangerous."

"I think one thing Facebook has to do is to try to get these totally fake news reports, that proliferated during the election, off the site," Lessin said. But, "I don't think you can win with human editors."

She said using technology, metadata and users flagging posts, Facebook could cut down on the influx of misinformation.

"But there is a lot of a gray area in what is true these days," she noted. "Everyday misinformation is being reported, and is it Facebook's responsibility to fact check that information? There is no way they can do it."

Facebook "is only one part" of the overall problem, she added.

Shares of Facebook were up over 1% Tuesday.

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