For example, if a school does not have a good record of sending kids to top college, will that reduce your chance?
No, it just says that past students didn’t qualify. Your student is not past students. He or she will get in or not based on his or her stats and profile. If your student has similar stats to past denied students, chances of admission are low.
Naviance is very inaccurate. As are any admissions predictions for elite schools. The school you go to is not as important as how well you do while you are there. Colleges take into account that your school has limited resources that you could not take advantage, on the flip side they will penalize an applicant for not taking advantage of the resources offered.