Ph.D. is training in how to do research. Solving one, even very hard problem not necessarily means that you don't need such training. It's especially tricky with counterexamples which sometimes question of raw talent and luck rather than skill.
The next step for someone who has PhD and want to stay in academia is postdoc. After solving one problem, you would not necessarily have what's needed to get a good postdoc, such as clear research agenda or proof of ability to publish consistently.
Modern PhDs are not designed for people that are smart like this. She's a math savant that obviously has a unique and demonstrably effective way of looking at things, why destroy that with "training how to do research".
I hope she's found a program that will support her while realizing she's smarter than whomever is setting the rules, rather than something stifling.
This is not true at all. Maths PhDs are excellent for this kind of person, and foster and grow such abilities. No matter how smart you are, training on how to do research is going to improve your capabilities and success.
The next step for someone who has PhD and want to stay in academia is postdoc. After solving one problem, you would not necessarily have what's needed to get a good postdoc, such as clear research agenda or proof of ability to publish consistently.