It's more like this. People think, not entirely incorrectly, that politicians lie all the time. At the very least, they cherry pick facts and statistics to suit their position. So given that for every fact you can find an opposing one and everyone else just seems to pick the ones they prefer, why not do the same yourself?
That's where alternate facts come from. She wasn't supposed to use that phrase publicly, but that's where we are at. The truth is the set of facts you cherry pick.