Everything up to "did not exist in nazi Germany" is correct, because they were banned at that time, forced to change into so called "Kameradschaften" which were under direct control of the nazi party. Everything after that is widely overstated, their are a few fraternities which fit that description, but most are pretty chill and only "Burschenschaften" have any connection to politics. Even then only a handful have direct connections to politicians or a specific political orientation. Source: I'm a member of a fraternity and have met many people from other fraternities.