It's more about reacting to being called a liar, I think. React with evasions or moving goalposts, and people will think you're a slimeball trying to fool them, even if you're not. Double down and stick to your guns, and people will respect you, even if they think you're an idiot, a liar, or batshit insane.
For me personally, authenticity is more about choosing to speak vs. laying low on certain topics.
Sure you can still lie when you speak to it, but at least you're being truthful on your desire to express.