If it was an open marriage, why would his first statement have been an apology to his wife and family? I don't see any reason to start assuming it was actually fine. In any case the affair becoming public in such a way would still be hurting them - the media attention you're speaking about. Much worse than a divorce, right?
Because the public sentiment towards open marriages is even more negative than towards infidelity? One is seen as a mistake that one can atone for, while the other is seen as a rejection of the institution itself in a country that has strong beliefs in it. Still only 65% of Americans support gay marriage, for example. Marriage following strict rules remains deeply important to a lot of people.