If you are shadowing surgeons at a “prestigious” hospital because this is of interest to you, or if you are planning to apply to BS/MD programs, go ahead. I would not do it for the purpose of impressing medical schools several years down the road because that won’t happen. Every applicant will have shadowing hours, you will need to shadow other types of physicians as well, and I can’t imagine that shadowing at a “prestigious” hospital will somehow be more “impressive” than shadowing elsewhere. I would think about the experience and what you learned, and not about the “prestige” of the facility.
Our HS has a research program and students have the opportunity to get published. It’s possible that this student has a similar opportunity.
I would still do the research, as every applicant will have shadowing hours. The exception would be if you are applying to BS/MD, where I think you need shadowing hours (?).
I would also be careful about using terms such as “prestigious” in your interviews and applications.