How are the top public schools having such a high acceptance rate compared to private ones?

The reason for this is because American Public Schools are State, not National like they are in China, S.Korea, India, Japan, or Western Europe. So a National University in China or India serves 1.4 billion citizens while a Public School in Pennsylvania serves only 13 million.

Take UPitt for example. Only PA residents can get the best deal applying as in-state applicants while if you live next door in NJ, MD, DC, or in CA, you have to pay out-of-state tuition. The same goes for all public universities. If you go to UCSanDiego in-state, tuition is $15K, and out-of-state it's $45K or 3 times the cost. When only a limited amount of applicants can benefit from attending a public school, that means that "demand" for that school is lower. So UPitt doesn't get a lot of applicants because there are other state options and there are many other better options for smart HS students. UPitt's Tower of Learning is a lovely example of American Architecture and iconic. But I think that most HS students would rather be in NYC, LA, Chicago, or Boston.

Depending on the ranking list you use, UPitt is #62 USNews #185 Forbes and #307 Wall St Journal. WashU is #15 US News, #26 WSF and #40 Forbes while NEastern is #44 USNews, #85 Forbes, #138 WSJ.

I think UPitts acceptance rate makes sense and so does WashU because it's consistently considered a top research university. NEastern is IMO over-hyped because their clout is more of a function of marketing manipulation like Tulane. In the Boston Area, clearly Tufts, BU, and BC are much better colleges than NEastern but they have gained momentum from a very aggressive ED i/II and EA campaigns that recruit over 75% of the incoming class early. They received close to 100,000 applications last year and it's rumored that the admit rate was more like 5.6%, not 18% as you indicated.

Intuitively, there is no possibility that NE should have the same acceptance rates as Stanford, Caltech, MIT, Harvard and Columbia but that's what happens when people hype up the brand like some luxury brand which it really shouldn't be.