Correct, not altruistic. Schools want the best students they can afford, and schools with huge endowments can easily afford to be truly need-blind in order to get some of those “best” (by their definitions) non-wealthy students. Schools with more modest endowments can be truly need-blind until the aid budget is depleted, to get those students.
So, Sportmom, do ask for aid at every school. Also note that need-blind doesn’t help if the school doesn’t meet full need (NYU for example). And run the Net Price Caluculator for each school to see if there’s a good chance you can afford it.