The history of, well... everything, seems to refute this: very little harm seems to come from digging in your heels even if you are factually wrong.

Most of the time you can lie, distract, and slander your way out of any sticky situation. The same biases that got everyone believing the original lie will take over and your support will be deepened.

And if anyone doesn't believe this, there is currently an elected official in the highest position of government of a major nation for whom this is modus operandi.

You would think that, but have you ever seen a politician before? (I careful avoid naming any one in particular, lest this get political)