Why are all the presidents members of those types of organizations?
People often ask this, but it could just be that people of high standing in the upper echelons of society and with political connections can become members of these groups. Similarly, only a person with this background and these qualities can become president or bigname politician. So it makes sense that the two positions go hand in hand. Both have similar "qualifications."
That might explain a correlation of sorts, but not why all of them are.
It could be that it's a very elitist group, and "somebody who's somebody" in the world of politics has to earn a place in one of these things. It's a resume builder. It would make sense that a guy who never made it into "American Cancer Researcher Society" (I'm making this up as a hypothetical) for his research credentials won't get a job in a cancer lab over a guy who did.