They don't have to be foreign. And tangentially, good propaganda is not recognized as such. For a borderline example, see how Call of Duty changed the attackers in the highway of death from the US to Russia [1]. But since it's only "inspired" by real events, they can claim they didn't falsify history, all the while contributing to a false perception of US forces.
Non-borderline cases are even subtler and more insidious, often indistinguishable from artistic intent, and can be anything from casting choices to subject matter (ever notice how some historical events get more attention than others?). Less overt, less coherent, but when so much media comes from California or New York, it makes their attitudes the default everywhere where that media dominates.
Imagine if the default, ambient culture, was shaped by Mumbai as much as it is today by Hollywood/New York. Yet even with your experience with propaganda, it slips under your radar. That's power.
[1] https://www.vice.com/en/article/mbmwgn/modern-warfare-the-hi...