Kudos to her for putting herself out there, but she's misunderstood what the point of this kind of application is. When you make a grab for a job like this, you underscore the fact that employers don't always know that there is something that can be improved - and that someone should be hired to do it. I vaguely recall someone writing an application for 37signals, where he made some redesigns for the site that he tho…
Her article/resume is her "show" not "tell". The medium is the message... that's UX.
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 doesn't show how she can help Instagram, and why Instagram would need her.
Maybe they have an available UX job position that I am unaware of, but she'd improve her chances if she directed her application to Instagram specifically.
Here is an exercise (for everyone): replace all instances of "Instagram" in the application with any arbitrary start-up name. There is little to underscore her passion and usefulness for Instagram (specifically) - she might as well have made the same website with five other domains with "Twitter", "Tumblr", etc. instead of "Instagram" in the URL and design. (She has that "No high heels" part, but that could be a variable to be replaced in every instance.)
This doesn't mean that I believe that she's done this(!), but a specifically directed application should be much harder to arbitrarily change to work for another start-up.
(I don't write all this to hate on her, as I've said in other comments in this thread, but there are some great, important lessons to be learnt. This is, after all, a great way to land yourself a job - if you pull it off.
Again, this will only help her career. It's just that it could be improved.)