If you receive a PhD from a university department, that department will think that it is too good to hire you as a faculty member. Instead, they lust after faculty hires holding degrees more prestigious than the one that they bestowed upon you.
This tells me the author has no knowledge of the academic hiring processes. Once you are at the stage of looking for tenured faculty jobs, your publication record is everything. If you're trying for a liberal arts school, then your research needs to be compatible with involving undergrads, and they care alot about your record as an instructor.
Professors all know how the PhD sausage is made, and are the group of people least likely to be impressed by prestige. They will just look up your actual thesis and critique it instead of relying on the halo effect.