I have heard dozens of people describe DNS this way, yes, like it's a push behaviour. I don't know how much it matters but I think making it clearer is good.
It's not what a user thinks of, but in terms of I updated a record and have to wait for it to be "everywhere" it's entirely part of the change latency to the end user and outside the scope of caching and TTLs being honored.
In the case of DNS, the information does emanate from the upstream server, but only upon request, like the ideas in the book.
I don't think anyone would phrase it that way, no. "Propaganda" generally involves things like mass leaflet drops, messages blasted out of public address systems, that sort of thing.