I'm not sure what system she would propose instead.
Edit: Seems a few people don't like the above comment. The application process anywhere will take into account grades, supporting statements, references etc. Not everywhere will do interviews but for those that do, it'll (presumably) be an additional point in all of this.
The only exception are the winners of nationwide competitions, who can enter any university they choose.
Oxford selects for potential, not for test results. How do they judge that potential? Well, they have developed detectors which are really advanced, carefully calibrated, extremely sensitive and incredibly difficult to game.
Those detectors come in the form of "professors" who have been teaching for 20+ years and know how to judge a student's potential from a 20 minute interview.
Disclaimer: I went to Oxford.
I do generally have a good opinion of Oxbridge, despite the fact they turned me down :)
It's the job of the interview to distinguish between those who have the potential to go beyond what's needed for A levels. For the most part, if someone has had to work extremely hard to achieve the top A-level grades, they're going to struggle at Oxbridge where the level is that much higher.
I'm not saying the current interview process is perfect, but test scores alone don't tell you enough to distinguish the best students.
Disclaimer: I went to Cambridge.
[1] http://www.bbc.co.uk/news/education-11012369
(edit: asterisk -> "star" to avoid italicising)
However, I would add that she does have a point about Oxford not being up to scratch (she should have applied to Cambridge instead ;)
Getting into Oxford is a difficult process and not many make it. Those that do have been selected based on merit, obviously she did not meet what the admissions tutors were looking for.
It's childish that she replied with such a letter to be honest, she just sounds like a spoiled child throwing her toys out of the pram.