> Two admitted her, but then higher-ups in those universities’ administrations overrode those decisions.

I've personally seen universities go both ways, and it comes down both to individuals, and to the culture of the department/university faculty and administration.

(Not to the culture of the student body, which is influenced by the administration culture, but has very little institutional memory, and almost zero power. If you draw an analogy to nations, there might be one with the most awful 'leaders' seizing and abusing power, but that's "way above the pay grade" of the many nice citizens you will meet -- who didn't know what they were being born into, and will do their best to be decent to each other, despite whatever bits they're unfortunate to learn about the upper powers.)