Earlier quoted context omitted.
Her article/resume is her "show" not "tell". The medium is the message... that's UX.
But what can she contribute to the Instagram team? Is their UX in dire need of a UX designer? It's fine as a resumé and general job application for everyone who reads the story, but she directs her application to Instagram - but it might as well not have been. It's not a lack of display of talent that I think is what she misses (although she tells a lot of things about herself that she doesn't show); it's that she do…
As far as demonstrate a problem that needs to be solved and how you can solve it...that would be a lot harder to do without risking sounding elitist and condescending. Maybe they don't have a problem that needs to be solved, they just need to do more of what they're doing. If she's a fit, they'll recognize that she can do that for them based on this site.