At least one famous research university states that (1) a Ph.D. requires the student to write a dissertation; (2) a dissertation is an original contribution to knowledge worthy of publication; (3) the dissertation will be judged by a committee with the chair and the majority outside of the student's department; (4) there is no coursework requirement for a Ph.D. Individual departments may have additional requirements, e.g., qualifying exams.

More generally a common statement of work being worthy of publication is that it be "new, correct, and significant".

Good research universities insist that their new assistant professors be actively publishing. Since not all of those professors have much success publishing, there do tend to be openings.

In some fields, people with good publication records can find jobs.

Some of what helps for a career as a professor: (i) Have teaching well enough organized that can do well teaching large, popular sections -- this teaching productivity helps the finances of the university. (ii) Be able to get research grants -- this also helps the finances of the university. (iii) Get a reputation as a leader in a popular field and, thus, contribute to the reputation of the university, which helps the university get gifts and, thus, also helps the finances of the university. (iv) Be successful at producing Ph.D. students that get good jobs. (v) Do well serving on committees. (vi) Don't be mean to students. (vii) Avoid politics and hanky panky.

For the OP, she (a) is finishing a book and (b) has been successful getting research grants. If the book can be judged to have content that is "new, correct, and significant", then she will have met the requirement "an original contribution to knowledge worthy of publication". In that case she may be well on her way to a Ph.D. in some good research universities.

There is an example: In the field of computational complexity in computer science, an algorithm that has polynomial time complexity is regarded as a good algorithm. This definition was from J. Edmonds. IIRC he had been a graduate student at the University of Maryland, left for a job, and published his research on network flows. The story is that, then, some of his former professors at the University of Maryland approached him and suggested, essentially, that if he took his papers, put them in a stack, and put a staple in the upper left corner, then they would accept that stack as his dissertation and grant him a Ph.D.

So, the story in the OP is not a fully new or strange as a way to get a Ph.D.

Colleges and universities like their professors to have Ph.D. degrees if only because that helps with accreditation.