I don't think there is any point to lying about it. The down side to lying outweighs any benefit.

And no, they don't have any duty, or really have any up side, to offering proof. As an American citizen you can demand proof, free speech and an inalienable right to scream at the wind, but they have no obligation or reason to offer any. Those who are likely to buy the idea that they are telling the truth already have; those who are not, will not accept any proof offered.

Earlier generation understood this.

Credibility is about telling the truth simply and directly and moving on. It is not increased by providing details and providing proof to every point. Explaining yourself undermines credibility by implying your word isn't good enough. People really don't need, or even really want, to know what goes into making the sausages. The crowd 'just asking' are pretty much all about having their target jump through flaming hoops to demean them and as light entertainment.