A dress code is a dress code. If you go in short, no shirt and flip-flops to a club they wont let you in. Why will the most historic/renowned/respected university in the world does not have the right to impose 'admission criteria', in this case clothing.
As a current graduate student at Oxford Uni (CS) I can only feel sorry for this girl. While the interview process is really serious (how else should it be?) I doubt that in any way she was treated differently in a negative way.
People know that Oxford and Cambridge have a social status to defend and maintain, as well as traditions that have been carried for hundreds of years, that need not to be change - or will be changed, because a goofy looking teen says so.
And just for the sake of demonstrating how full of shit this girl is have a look at this letter (originally from reddit) where an almost identical letter was used for a _job_ application. The only thing this girl did was ammend it to be address at an academic institution.
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Herbert A. Millington
Chair – Search Committee
412A Clarkson Hall, Whitson University
College Hill, MA 34109
Dear Professor Millington,
Thank you for your letter of March 16. After careful consideration, I regret to inform you that I am unable to accept your refusal to offer me an assistant professor position in your department.
This year I have been particularly fortunate in receiving an unusually large number of rejection letters. With such a varied and promising field of candidates, it is impossible for me to accept all refusals.
Despite Whitson’s outstanding qualifications and previous experience in rejecting applicants, I find that your rejection does not meet my needs at this time. Therefore, I will assume the position of assistant professor in your department this August. I look forward to seeing you then.