Are these people genuinely her friends?
Yes, they are. (some of us have hung out with her in person, as well, for whatever that's worth)
Does the social media even have the capacity to provide anyone with the valuable interpersonal connections that we all need in order to maintain an adequate level of mental health?
By itself, of course not. But as another dimension of human interaction, it's certainly supplemental. Meaningful, lasting relationships can & do develop in this abstract realm all the time.
It is a telling fact that despite the proliferation of technology that grants us opportunities to cultivate online relationships with other people, our social capital is plummeting precipitously. Robert Putnam covered quite a bit of that in Bowling Alone and he was mostly right, online communities are at best distracting us from opportunities to create rewarding professional and interpersonal relationships in a face to face setting. It creates an illusion that exacerbates the plight of the alienated youth.
I think this subjective topic is difficult to pin down in terms of statistical or universal absolutes. To some extent, it depends on how one chooses to live (one might also factor in where an individual lives, & under what conditions, as sometimes more interaction with the external world simply isn't as readily available, for various reasons). People can & do successfully maintain fulfilling relationships on each of these planes in tandem. Of course, interacting exclusively in online communities & literally never making an effort to engage with those in your immediate surroundings would not be conducive to healthy psychological growth; I think most people here would agree.
I admire the typological ingenuity on your part, after all, any "INT" with an odd sense of humor must have asperger's syndrome or suffer from autism, right?
No, unfortunately, that's not correct: all of the counselors I've visited (when I was a regular forum member), certified that I was perfectly mentally healthy and entirely devoid of personality disorders.
Ah, you're not familiar with my lame humor, I see. Allow me to clarify. I call INTx's "aspies" with utmost affectionate humor. Some of those closest to me happen to be INTx people. Diagnosing mental conditions based on type alone is absurd, hence the joke. My delivery isn't always well-recieved; hit or miss (ironic, since I'm making cracks about the social clumsiness of others).