The issue of internet-mediated persona versus real-life person has been around since long before the advent of social media, and I think it's a lot more complex than simply that the former is fake and the latter genuine.
The internet's a different place, sure. You're physically and temporally dislocated from the people you're interacting with, allowing great scope for manipulation of the image you put out. You can pose on Craigslist as a member of the opposite sex, or pretend to be a Nigerian prince, or just act like a belligerent arsehole with little fear of repercussion. And the way we communicate is definitely different - I don't usually talk like this in real-life. I swear a lot; I pause and say "um", I mispronounce words - communicating on the internet in false-time allows me to slow down and consider my words and sentence structure, and try to make sure I don't make any mistakes.
But I don't swear in front of my grandmother. The idea that communication on the internet is somehow intrinsically fake (and the corollary that offline communication isn't) has never rung true for me. Online interaction is a particular kind of mediation - so is pretty much every space in life. The internet just offers a capacity for performance that is usually impossible in real life - a meek 15-year old nerd threatening to murder another player in a game of League of Legends, for example. Equally, though, this form of mediation allows for a great amount of openness and sincerity; people are often willing to share things with friends online that they would almost never say online. It just goes both ways.
We are more or less constantly mediated by the circumstances in which we find ourselves. As I said above, I don't swear in front of my grandmother. That doesn't mean that the "real me" doesn't swear (and that doesn't mean that the non-swearing me is not the real me).
I teach English as a second language in Dublin. Mostly I teach junior groups; Italians of 16-18 years. I was chatting to a couple of the other teachers about how we act in class - re-using the same jokes over and over and acting as if they're spontaneous. Sure, it's a bit facetious. But I just said goodbye to a lovely group of students today and the connection we had was not somehow unreal.
When I'm at work I wear a shirt and slacks and black shoes. When I went to a staff party at a pub last summer, I wore jeans and a leather jacket and had my septum piercing out. Some of my colleagues were a little shocked at this difference, but it doesn't necessarily imply that my "work persona" isn't me.
When I'm at home in Mayo I talk with a Mayo accent. This also happens when I'm drunk.
I write letters to people quite a lot. I imagine I sound quite different in them. The manipulation of one's image that takes place in writing on the internet, whether intentional or otherwise, is not new.
Is the real me the me talking to you late at night in a dark room talking about serious issues in my life? Sure. So is the me making bawdy jokes. So is the me sitting alone in my room typing into Hubski.
We perform constantly, in many different contexts. That doesn't necessarily mean that none of that counts as "real". Mediation is more-or-less ever-present, whether online or offline. I don't mean to go all hippy on you and suggest that people are super-complex chimaeras or shape-shifters; there's plenty of consistency. There's also plenty of seeming inconsistency, but lack of consistency doesn't imply that certain parts are fake and certain parts are real.
People certainly act "fake" on the internet at times, but we've been doing that in real life for thousands of years. But I suppose all of the above is a fairly pointless aside because the ultimate point of the article is basically true - online and offline personas, even if they're equally "mediated", are often quite different, as anyone who's met someone online and then in person can tell you. And also I seen to have veered way off the topic of the differences between how people present themselves on social media and how they act offline. Sorry if I'm not particularly lucid; my brain has pretty much turned to mush in the past two years.
(Yeah I'm totally different in person BTW.)