I am sure, that while they may not have been of Greek Social Organizations, they were members of the Masons!
Starting With George Washington!
The reason is that most were in a battle of some kind and need a Brotherhood who could and would back them in times of striff.
People they could turn to for advice and counsel!
Sound familiar for even today?
Little did I know back when, that when I knew H S Truman that he would be a Brother of mine as well as my President!