I can definitely understand your thoughts. However, the financial talk showed that students average around 200k, not 300k in debt after leaving. Not that 200k isn't really high, but it's definitely not 300k. They will support and help you find outside financial aid/scholarships, and 37% get institutional aid.
Also, DC is expensive, but if you choose to commute a little (or a lot, depending on how much you want to save) instead of living really close to the school, there are less expensive living options. For example, if I go to GW, I'm considering living in Northern Virginia, which is on the same metro line as GW and could cut some costs (as opposed to living in the area that GW is in).
It is expensive to attend GW, but it doesn't have to be 300k. Hope this helps!