So this one time, our main customer database fell over. The primary key wasn't wide enough, we hit 2 billion rows, and everyone panicked. We had been working unwise hours for several days, and we got the fix together, and I made a mistake: I pushed it directly to production. Man, my boss was really mad; no one had been getting enough sleep and we were all stressed. I apologized profusely and said it would never happe…
In such a situation, multiple mistakes were made. If that work culture could somehow support honest, open, and humble approaches to understanding the problem, there would be multiple people either apologizing or, better, taking ownership of their contributions and working towards preventing them in the future (the thing you identify that did not happen). Such a culture is, unfortunately, very unlikely due to the incentive structures of company hierarchy.
The role and power of the individual for whom we're setting these expectations is very important and it's very unhelpful that this isn't considered either in that wiki page or in so many comments (not yours, yours is good). Is the person that made a mistake very powerful and do they have a PR team? Their approach will probably be purely cynical. Is it a company? We should stop anthropomorphizing companies. Is it a junior colleague? Was it truly a personal error on their part or higher up or systemic? Was it a manager harming an employee? On a moral and societal level, we have to consider those harms and whether owning a mistake and apologizing is desirable or even sufficient - perhaps they should just be fired or we should consider their actions to be a crime. Or maybe "we" in this scenario is again PR thinking intended to protect the company, in which case the apology is carefully wordsmithed to avoid liability and has no real value.