I don’t think that schools are being dishonest when they set their tuition prices. Tuition is set by operating costs, which are dependent upon cost of living in the location, as well as the type of facilities they have on campus. Most of the schools mentioned on CC have state of the art facilities, and those come with high price tags to maintain properly.
The other major factor in tuition prices is supply and demand. I can think of several schools whose tuition is significantly lower than the typical Northeastern schools who are mentioned here on a daily basis. Valley Forge Military Academy, Church Farm, Phelps, West Nottingham, Christ Church School, to name a few, have lower tuition than the average NE boarding school. These schools may have qualities that do not appeal to as many people, such as being military based, or single sex, or almost fully international, or very low (below 30%) boarding population, or dilapidated facilities, or a combination of above factors. Perceived quality of academics and boarding experiences may be lower than the well known schools. Lower demand makes for lower prices.
My SIL lives in the Deep South and looked into several BS in southern states a couple years ago. Most were tiny schools, had small boarding populations, and significantly lower tuitions based on location and the schools’ needs to attract students.