What is ‘based’ based on?

‘Is it connected to plant-based?’ asked my husband, as though we were playing Twenty Questions. ‘Anything to do with Homebase, drum and bass, Prisoners’ Base?’ I was trying to interest him in the 21st-century meaning of based, of which he had never heard. The New York Times never stops trying to give a new etymology for based, according to Jeff Bercovici, who is co-head of the newsroom of the San Francisco Standard.