1. In some fields, it is possible for a graduate student to have their article published in a respectable journal, while in others that is very very rare.
2. Of course, jointly authored articles with their advisor/professor are more common and more likely.
3. As for Independence: While we might expect a junior faculty member coming up for tenure to have developed a research path that somewhat different than their teachers and advisors, it is rare if ever that happens with doctoral students. Doctoral students usually work within the purview of their advisor's field of interest and research program.
4. As for Originality: If you are working at the forefront of a field of research, you cannot help but be original. It's no big deal. If you are replicating earlier work since it was not sufficiently credible, or going over a long-standing problem, in general you will exhibit originality in the quality of your work.
5. While there is a demand for a publication or two by graduate students, in some fields, when they go looking for a job, I find that hard to believe, unless the field is not very deep. (But see #2 above.)
6. Home run papers: The baseball analogy is quite prevalent in economics and business, and perhaps in some other fields. I never hear about them in physics or mathematics, or the humanities, or most of the social sciences.
a. Make sure that the home-run paper is actually the responsibility of the candidate, rather than a joint production with more senior authors.
b. Really significant work that has high impact usually demands some years of maturity and experience beyond the doctorate and the assistant professorship.
c. I don't know if the baseball analogy is appropriate for scholarship.