"Also, the assumption that boarding school teachers can’t afford the tuition is pretty close minded. "
No one was making a judgment here. Bottom line is that the salary of a faculty member, with the exception of some higher ups, falls below the threshold for full pay. But of course spouses often work, some have other financials sources, etc. It becomes moot when faculty get an employee discount anyway but, yes, many would qualify for at least partial need based aid.