From the paper: "Since our results are drawn from data on a single college, they may have limited external validity." In particular, they specified that this college is a small liberal arts school. I too was in a fraternity at a small liberal arts school. I think people should be wary when trying to paint the national fraternity system with the same brush stroke, as the greek climate at small liberal schools can be quite different that the climate at large universities. I'm not sure how this would affect their results, but the environment is very different in my mind.
They also say: "57% of alumni in our sample report belonging to a fraternity, which is somewhat higher than the 46% of all male alumni that were fraternity members. Greek alumni may be over-represented in the survey due to greater attachment to the college." While they mention this detail in passing, I find it quite interesting. Not sure what the implications are; it would probably require further study.
I'm also not quite sure I buy that people self reporting the amount they drink is controlled by adding their age and age squared as factors. I think it's natural to remember the "good times", which often coincide with drinking, but not remember the weeks you spent slogging through coursework. This, sometimes combined with a perverse incentive structure that says drinking is cool and you should do it more, may artificially inflate the self reported number of nights in a week spent drinking.
I also see a lot of people in this comment thread saying the increased salary is intuitive due to the connections made in a fraternity. I am suspicious of this. This is anecdata, but I was one of two computer science majors in my fraternity (of ~75 members). I have received no obvious professional gain from being in my fraternity. A number of my other friends who went to med school, dental school, and law school had to get in on their own merits -- fraternity connections do not apply to those domains (alumni ones, perhaps, but not fraternity). Others who got jobs seemed to rely more on connections between our college and various companies, not through our fraternity.
It's unfortunate that this paper does not control for college major -- they do when considering the grade regressions, but not the future salary. I would imagine the distribution of majors for people who are in a fraternity are different than the distribution of majors for those who are not. Perhaps those majors chosen by people in a fraternity, like law or business, tend to be more lucrative. Additionally, I can imagine people in some of the more socially conscious majors might be repulsed at the idea of joining a fraternity, and also do not tend to be the highest paying. I am being a bit broad and hand-wavey, but this comment is not a research paper -- just trying to capture my intuition.
Lastly, relying on my personal experience, I think a fraternity might improve qualities necessary for working at a company. Again, anecdata warning, but I became more sociable and confident after joining my fraternity; I also became less edgy, awkward, and bashful. I think these qualities are some of the intangibles that can help people get ahead at a company. Perhaps most importantly, you are forced to live and work with some people who you dislike, which is essential for being in the workforce.
All in all, I think it's an interesting paper, and I appreciate their work. It still leaves something to be desired though.