Hey! My daughter goes to Krug's school--over $40ooo per year--but we aren't exactly propping the school up financially: she is on an approx. 90% full scholarship! So she's just taking up a place that might've been taken up by a lib. if we'd boycotted the place!
The school is still directly or indirectly getting cash. Schools that don't have a lot of top students attract less in the way of earmarked scholarship donations and general endowment fund donations. The school is benefitting financially by your daughter being there. Not as much, or as directly, as if you were paying the full bill, but still plenty.