I'm sorry for continuing to respond to this, this isn't out of malice but true intrigue. In San Francisco, outside of Lowell, we don't have the elite merit based public schools a place like NYC does. So everyone sends their kids to private school. At least within my circle of acquaintances, where you're going to send your kid to school comes up a lot in discussions including are you using a consultant or anything else to try and help.
Being SF, it's not uncommon to hear a fair amount of anti-Trump rhetoric in these types of conversations as well. But never have I heard anyone say Barron Trump went to private school.
Where does that come from? My wife often asks how my brain works. I'm asking you the same question here.