A PhD by publication sounds very similar to a higher doctorate (DSc, DLitt, etc). Substantive (as opposed to honoris causa) higher doctorates are awarded based on publication record only. To be eligible for a substantive higher doctorate, you generally are expected to have a PhD first - but it might not be an absolute requirement. You’d generally expect a bunch of papers, but in principle a single publication (if sufficiently groundbreaking) could be enough. While this is very impressive for a 17 year old (I wish I could have done that at 17, or at any other age for that matter), it probably isn’t significant enough for a higher doctorate all by itself. If she’d proved P=NP, different story. (Who knows, maybe she shall-well, probably not, but I’d be very happy to be proven wrong about that.)