According to this it is a non-profit corporation open to the public. A corporation is just a legal structure around ownership interest. The corporate shareholder structure allowed the shareholders to collectively share their books in the library which they provided to the public. Nothing about being exclusive to the rich.

Income is a continuum. Schooling (not to be confused with education) at its essence is just a room with a teacher, pupils and study materials. It can be realistically attained by nearly all income levels but the extreme lowest.