That's part of it. Private schools also have some advantages that make it a little easier to implement safety measures (I still don't personally think those are enough to make going back the right idea). Public schools will be limited in their ability to enforce distancing and mask-wearing, Private schools have much more disciplinary leeway. Many private schools also don't have the same special needs populations or the attendant legal and ethical considerations. Special needs students are going to be the toughest to keep distance, with behavioral, physical, medical, and toileting needs that necessitate close contact. Some groups of that population will be very difficult to get to wear masks. Asking those populations to stay home when their general education peers are in-person is problematic in many ways. Private schools also don't have a well-funded teachers union and their legal staff to contend with on issues of teacher safety.
Are you just as willing to follow their second statement, released after so many misinterpreted and misused their first statement? Nobody is arguing with their original point, that in-person instruction by qualified teachers is best for children. They also point out that without additional funding, additional precautions, and attention to safety, it's not just a blanket good idea to reopen schools. If you read your link carefully, you'll see they're not being prescriptive, they're simply saying that every effort should be made to safely reopen schools, not that it's currently safe to do so. Here's their follow-up:
https://services.aap.org/en/news-ro...dents-urge-a-safe-return-to-school-this-fall/
Would you be open to considering those factors in who is allowed to return? That 20% you mention are at much greater risk and much higher need of the benefits of in-person schooling, but the loudest voices for reopening right now are parents who don't have internet access issues. In my wife's district, most families with a stay-at-home parent are planning to send their kids back, I'd like to see that option reserved for the children of families where at-home options are impossible. The people with the money to hire lawyers will make it untenable to help the neediest.