No, Zionists--and let's be specific here, we're talking about AIPAC--absolutely do have an outsized influence over American politics. Just look at how they brought down Jamaal Bowman, just one case out of many.

They may not *control* the American population, but they absolutely control the "narrative" and hence the political reality.

Other than that your last sentence is correct. (But think about that second word; whose propaganda?)