There will always be people who disagree with you, and who will continue to make public attacks on you. They're not the ones you are apologizing to, or for. Pretending you did not make an error will eventually catch up to you, in the opinions of those who would view an apology to your credit and in the fact that it leads to you making more mistakes and not correcting them.

"...absolving the mob of any evil when they pull the person apart limb from limb."

That's a little excessively dramatic, don't you think?