Yes some professions have bigger consequences for mistakes. If you can't deal with it go do something else. Not an excuse for covering up your mistake. This is downright Orwellian.
Second, a "cover-up" is when you hide evidence of your past misconduct. Pleading guilty in public is in every possible way the literal opposite of covering something up. If they'd just deleted the article with no commentary at all, that's covering up the mistake. Leaving the original URL up with a notice that they erred in publishing the original story isn't.
Besides, it very may well have been demanded by their legal department to avoid any repercussions from the mischaracterized party.