I think I'd agree, especially with regards to the article's Step 3.

Admitting fault can open one to liability (sometimes legally). Although perhaps it depends on how one defines a mistake versus, say, an outright fault that people could find morally wrong.

An example that's not perfect (and I'm not arguing/defending one way or another) is Louis CK with the #metoo movement.

It seemed to me that his response was sincere and correct on the personal level. He acknowledged those he'd wronged, made clear the victims were in the right, apologized, and expressed a desire to improve his behavior. For all that, he was demonized.

To some extent, it felt like people were saying: "My god, you admitted it. You're worse than Harvey Weinstein - at least he had the decency to deny his actions."