Yale University isn't responsible for these societies and has no control over them. They occupy private property and by their very nature lack any formal institutional affiliation with the school. They're simply private clubs where current and former students can hang out and plot the next global financial collapse, have orgies, or whatever exactly it is they do. In any case, not Yale's problem - except an image problem, maybe.
As an alumnus, I find the hand-wringing over these societies weird, because they're completely irrelevant to most students and have been for a long time. (No, I wasn't invited to join one. I don't even think I knew anybody in one of the name-brand societies, at least not well.) The fact that Bush and Kerry were both Bonesmen was amusing, but hardly surprising - the societies are exactly where you'd expect ambitious, privileged social climbers to end up by senior year. They're not even very secret, since the membership lists inevitably leaked. The only time the rest of campus noticed is when they walk past one of the "tombs" - windowless clubhouses - or when a really terrible movie about S&B ("The Skulls") came out while I was an undergrad.
Are they creepy and elitist? Of course. Are they a sinister conspiracy? No more than Goldman Sachs or McKinsey.