But the concept of granting admission based on such status, as opposed to extending special treatment to an admitted student, is very much muted.
There are ways of getting in to a university without passing the gaokao threshold that would ordinarily be required. But those generally involve receiving a point boost that the college has the official discretion to offer, or doing well on an alternative test -- someone scoring 303 out of 750 would obviously not pass a lower discretionary threshold either.
Note that when "officials in Shandong say new processes are now in place to make sure such incidents will not happen again", they are correct -- it's already possible to look up both your gaokao score (this girl's score wasn't falsified; rather, her identity was stolen) and the 分数线 that applied to you when you applied to a school. The problem would be instantly detected[1] by anyone who felt bitter about what happened -- and this is quite likely, since you have a strong idea of what your gaokao score will be before you actually take the test. (You have to, because you apply to colleges before you get your official result.)
[1] Well, detected with probably a one-year lag.