Just ask the folks at Uber. One of their executives said something that was pretty horrible (he was going to spend a million to smear anyone who wrote something negative about him). His boss, the CEO of the company, responded by apologizing via Twitter. You can see all 14 tweets here.
He did the right thing by apologizing, but he must know by now that the Twittersphere does not accept apologies. They keep going until someone is fired.
