As others have pointed out on Twitter, I am not sure who is the victim here; Nidhi Razdan apparently had multiple speaking engagements where she was introduced as Harvard faculty:
I don’t understand. Are you saying people are claiming she made the whole thing up and was just going around saying she was an associate professor at Harvard?
To be honest, NDTV is one of the top English channels in India and Nidhi Razdan is a very well respected and recognized journalist.
It makes no sense for her to fake all of this for some "clout" as some on twitter suggested - she does not need it. Unfortunately there is a lot of cynicism for anything media (and in turn politics) related in India and people love to speculate.
What you are suggesting here makes this already interesting story even more interesting. Perhaps there are holes in her story but if she really knowingly faked the whole thing, why would she resign from her job?
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.)