What counts when making a headline apology?

We see a lot of these all the time. Politicians, celebs, police, etc.
Someone will make an apology that doesn’t seem to cover the definition.
“I’m sorry you can’t take honest criticism.”
“I’m sorry you found my words/actions offensive/deadly.”

And there is a call for a better apology.

What is the criteria for a public apology?

Sincerity is important, as is admitting that what you did was wrong, accepting full responsibility, and vowing to make it right. It’s also helpful to make the apology soon after the accident. You need to basically say, “I fucked up. It’s entirely my fault, and I accept full responsibility. There’s no excuse for [whatever egregious thing I did]. I’m an idiot. But I’ve learned from my mistake, and I will never make it again. I will also work to make it right.”

You should also add into your list of non-apologies the next stage, which admits wrongdoing but absolves the utterer of responsibility: “Mistakes were made” - though not by me or anyone in my department.

And expressing “regret” without actually saying sorry. “We regret the deaths that occurred” - where by “occurred”, the speaker means “were caused by the bombs we planted”.

It’s funny how the apology Mayo Speaks! mentions is so obviously the most sincere and effective one, yet how bloody difficult people - even slick, polished politicians - find it to do.

The funny thing is that several of the most recent celeb apologies have had all the elements mentioned and yet are still rejected and derided by their critics.
I suppose the actions simply speak louder than the words.

I wrote a blog post on the subject a few months ago, describing four easy steps to apologizing like you mean it: