Again, you're confusing "lying" with "bullshitting". Lying is about establishing belief in a false version of the world, which is best done, as you point out, by omission. That's because lying depends on peoples' regard for the facts; it exploits that. Being caught in a false assertion destroys a lie's effectiveness, so a smart liar sticks to the facts.
Bullshitting is about inculcating the desired feelings and attitudes in the audience. While a bullshitter doesn't hesitate to use facts when they suit his purpose, he doesn't hesitate to make shit up either, because it doesn't matter if he's caught. It doesn't even matter if he asserts two inconsistent things in the course of a single sentence.
Because bullshitting doesn't aim to establish belief in propositions; propositions are completely disposable. Once it has done its job, a piece of bullshit (unlike a lie) is a nullity. You can show that it is false, but the bullshitter's adherents won't perceive that as inconsistent; not as long as the bullshitter is conveying the same attitude.
That's why fact checking a bullshitter is a waste of time, once you've established that's what he is. It doesn't matter if you prove something he said was wrong, unless you do it in a way that changes his audience's feelings.