Seattlecyclone, I don't know whether you are taking a stand for people who truly need assistance or whether you think that this case is worthy of assistance. If the former, there is no disagreement. If the latter, and if this is a privileged college graduate with family (including relatives close by) who can help, then this is a judgement call. this kid has many options, including not living in the middle of a very HCOLA. public assistance, housing, and other welfare benefits should really be reserved for those in need. It does not sound as if this kid is in need. If he is, then let's hear it from the op. But if he is not, and you would still suggest that he take benefits that are intended for the needy, then your priorities are not in line with the thinking of the general public in America. At this point, I think you are simply arguing for an abstract which doesn't seem to apply in this case.
I suspect the OPs cousin would not want to accept benefits that are clearly intended for the less fortunate if he is in any position to do so and with his education, and the labor market in DC I highly doubt he's in a poverty situation.
As for your argument, every college student takes reduced or no income while in school because they see more opportunity on the other side, yet public assistance is not available to students except in rare instances such as head of household, etc.