Also, it is unusual for a dissertation to be outright rejected because of how it reflects on the advisor and committee: the committee is (supposed to be) kept up to date on the student's progress and will recommend against defending if the student is unlikely to pass. Slightly less unusual would be a student being allowed to defend, but then needing to do major revisions to their dissertation for it to be accepted. Keep in mind that at the point one is defending, quite a bit of time and money has been invested in the candidate so there is a good incentive to see the candidate succeed for no other reason. Unsuited students are (ideally) dismissed much earlier, i.e., at admission to candidacy.
One absolutely worries about being scooped on papers, since those are the currency of academia and being scooped usually results in needing to publish your own (now less novel) work in a lesser journal. And as another commenter points out: a professor taking on 10 students with only 1 succeeding, if one defines success as being tenured, isn't that far off from reality.
As an aside, I personally think forming a research group at a university isn't all that different from creating a startup.