I suspect people assume propaganda is only propaganda if there's a centralized "Ministry of Truth" that (a) has one coherent message, (b) is controlled top-down from a central authority, and (c) has police authority to silence deviations from the playbook by force.
As with so much in Western capitalist democracy, America's style of propaganda doesn't fit that authoritarian rubric, but it ends up having similar effect. Major differences are (a) different departments of the US government are protecting their own interests; to the extent the message is "one coherent", it's the principles baked into the institutions, (b) control is decentralized (every department has its own PR budget), and (c) rather than coercion by force, it's coercion by incentive; if you want the opportunity to get your movie "super right" by having professional on-site advisors or access to authentic hardware, you play by the providers' game (and you do want that, because you believe your audience wants that).
House of Cards made me realize something very self-evident: the baddies in "realistic" entertainment media do not reflect the baddies in real life (ditto for the good guys, for that matter). I saw one day that I was conflating real world and HoC politics. Not the actual events, but rather how the different actors got or lost their way. Since I don't know what's going on behind the curtains, I started filling that gap in real-world knowledge with constructions based on the personal politics portrayed in HoC. Now, I try to be as suspicious as sanely possible of anything even remotely tied to politics, and yet it took me a month to notice my error.
What happens in minds that don't? I suspect they imagine the real world functions like the dream worlds created in studios. I think that's the insidiousness of propaganda you're describing.
I loved this newest season of House of Cards. There is a lot of political commentary in the form of allusions to real-life people and things, and some of them fall into what is considered "conspiracy theory" (e.g. a Bohemian Grove / Cremation of Care reference).
I don't see it as being that close to reality in every way, but the central message of this season is something I've been trying to communicate to people for a long time. In my interpretation, that message was of the government being captured by the war industry and of those captured factions using and even manufacturing terrorism to goad the public into war. Frank Underwood's rise to power is plausible in a political climate like in the US, and the scenario of a corrupted president retaining power by forging a deal with the war industry is also plausible IMO.
I don't pretend to know exactly how it happened, but there is no doubt that something similar is going on in the US. If anyone can offer me a coherent narrative for G.W. Bush's Iraq war with consideration to the 9/11 "28 pages" and related evidence, Obama and Trump's sale of hundreds of billions in weapons to Saudi Arabia, a never-ending state of war without need for congressional approval, the extreme erosion of civil liberties in the Patriot Act, 2012 NDAA, etc., then I am keen to hear it.