You hear this about Brexit, climate change, bankrupting the government, violence and war, etc. It's the same rhetorical tool used for a lot of propaganda: You can lie in a moment; it takes hours or days for people to gather the evidence to disprove it.
(To disarm this propaganda: It's easy to construct nonsense that sounds plausible - even to you, smart person; don't let your ego be your weakness - and professionals make a study and art of it. Don't take anything seriously unless it has serious evidence and research behind it in the first place; the first claim has the burden of proof. Also, notice that their real argument is in the unspoken assumptions behind it, how the issue is defined and framed.)
Here's why I think it works: Most policy consequences are difficult to notice if you are uninformed. You can't know nationwide unemployment, GDP growth, or climate change by looking around (with some exceptions). Western economies and societies are huge and complex; often changes are subtle and slow; often they affect one set of people - probably not you - more than another set of people. Finally, in an environment that complex, it's hard to provably connect outcomes to actions (is that hurricane due to climate change? did people get cancer because of the factory's carcinogen or because of bad luck?), and the propagandists can pump out enough lies to raise doubts in people's minds (look up "FUD").