Well, you do have something of a point here: if you have done something that is illegal or widely regarded as reprehensible, then it is usually in your best interests to deny it - but it is quite obvious that the article we're all nominally discussing here is not about such situations.

I also find it interesting how the issue of admitting to making mistakes is being conflated with apologizing. While they are related, there is an important difference: a person who will never apologize is merely immature, while one who never admits to making mistakes might be a dangerous liability to himself and others, and is unfit for positions of responsibility.