[JamesianP]

Coding is not a great example. It can be fixed silently and the error disappears, unlike published claims. And I'd say you're making an analogy that is extreme. The corrections we are talking about are shared in the same forum the error was shared. If you had presented the mistake to the CEO or on linkedin then it would be appropriate for the error to be pointed out there too. Otherwise the audience will remain misled.

If it's some minor code bug from a typo or something, your embarrassment should be correspondingly tiny. And still the right thing to do is say "thanks" or "nice catch".