I'm not sure why Bettman has to apologize to Beach.
Campbell's contention was more about media positioning Bettman's statements as an apology.
As for whether an apology is actually owed, I believe what is truly owed is a thorough audit and subsequent action to ensure the League has the mechanisms and people in place where such a violation and dereliction of duty does not happen again. Not only is it the right thing, but for the future protection of the League's reputation. The NHLPA doing the same can only be a good thing. They're not going to be doing that under Bettman, as his modus operandi is to try to keep things quiet and boring.
Poop rolls to the top, and the League is responsible for the conduct, and to some degree the culture, of its franchises. What has come to a head in this case is the decades of general coverup of issues (domestic issues, substance abuses, assaults) leading to the series of wrong decisions the Chicago hockey organization undertook regarding Aldrich's abuses.