Can you see a 12-year view of your school’s history with each university? I can see that on our Naviance.
Also, yes, our public school supposedly never gets any admits to Duke. On the contrary, about 5-6 students a year (usually athletes) get into Duke from a nearby prep school. I think Duke does have its favorite high schools/prep schools.
However, things are continually evolving so you never know - just wait and see. Good luck!