I’d phrase it more like if you attend a “selective” high school, your high school is more likely to have a large number of highly qualified Ivy applicants, which increases the chances of multiple Ivy admissions. If you attend a non-selective high school, your high school is less likely to have large number of highly qualified Ivy applicants, which decreases the chances of multiple admissions.
While high school selectivity is a key factor in number of Ivy admissions, there are other important factors as well. Another important one is location. If your HS very close to an Ivy, you probably have a large number of applicants to that Ivy, dramatically increasing the chance of multiple acceptances. Location also influences the concentration of parents and others with higher education background, who strongly encourage their children to value the same. I previously mentioned how Cornell was very popular at the basic public HS I attended in upstate NY. Cornell receives more applicants from my former HS than all other Ivies + SM combined, perhaps more than any other private college. According to Naviance, my former HS gets several Cornell acceptances and matriculations each and every year. The acceptance rate is similar to the national average. Instead the large number of acceptances more relates to the large number of applications.
Another important factor is wealth of the area. The study at https://www.brookings.edu/wp-content/uploads/2016/07/2013a_hoxby.pdf reads, “We show that the vast majority of low-income high achievers
do not apply to any selective college.” If the vast majority of kids from your high school do not apply to any selective college, then your HS is not going to have many selective college admissions. In contrast, students from wealthy areas have a much higher rate of application to selective Ivy-type colleges than the national average, after controlling for test scores and other measures of academic achievement.
Another important factor is public high school vs private high school. Students are more likely to apply to and attend colleges with a similar public/private classification to their HS than average. Public high school kids are more likely to apply to public colleges than average. Private high school students are more likely to apply to private colleges than average. The same could be said for “elite” private high schools and “elite” private colleges.
School quality measures can also be important, particularly in relation to GCs, teachers, classmates; and others encouraging Ivy applications School quality measures can also influence things like more opportunities to pursue and excel in areas colleges value, more likely to write excellent LORs, GC has more time to advice a particular student, etc.
In short, Ivies can and do take more than 1 student from particular HSs; and the minority of high schools that receive larger number of acceptances are largely predictable based on a variety of HS and community characteristics. However, the majority of public high schools in the US average well under 1 acceptance per year at a particular highly selective college, so multiple acceptances per year are often very rare.