It's possible there's an innocent explanation but Occam's Razor does suggest she just made up her Associate Professor at Harvard title and, when called out for it, concocted a story about it really being Harvard Extension School and phishing. Which was vaguely plausible so long as you don't think too deeply about it and ignore that, if this were the case, the initial Twitter post was deceptive.
By “resigned” I am assuming you mean she was fired. If she were fired why would her previous employer allow her to use their website to publish this story?
Who knows? Maybe the Occam's Razor conclusion isn't in fact the right one. Maybe the publication thinks it saves them face as well as her. (Journalists who lie look bad for news publications even if they're fired.)
It's possible there's an innocent explanation but Occam's Razor does suggest she just made up her Associate Professor at Harvard title and, when called out for it, concocted a story about it really being Harvard Extension School and phishing. Which was vaguely plausible so long as you don't think too deeply about it and ignore that, if this were the case, the initial Twitter post was deceptive.