I also found this confusing. The interpretation that I came up with which made sense was that "They don't!" is meant to mean "mu" (being an interjection to say that the premise of the question is false) and that "large institutions" is a stylistically unqualified reference to public-benefit institutions directly supported by individuals. The false premise is that large (individually-supported, public-benefit) institutions exist, from which we could ask how.

The double whammy was momentarily confounding and a bit fun, but resulted in some forum heat loss and annoyance.