>You're assuming that the idea is so sticky that you can't avoid it if you hear it.
Often times, it is.
Many people who fall into conspiratorial thinking believe themselves to be the victims of elaborate campaigns of propaganda, mind control, gaslighting, etc. Many also reject the mainstream rationales behind arguments against their beliefs as being fallacious or misinformation, and interpret attempts to convince them otherwise as validation of their fears.
Such people don't arrive at their beliefs by logical inference, their conspiracies serve an emotional need, similar to belief in cults or extremist religion. It can be comforting to "realize" there are puppetmasters pulling the strings behind the mundane chaos of the world, and that you alone can see the facade. Even if those puppetmasters are malicious, you know they're there, you know there's a plan.
Conspiracies are about making sense of a senseless world, and that's why it can be difficult to turn people away from them. No one wants to live a meaningless life in a world of arbitrary and ultimately purposeless cruelty.