While the specifics of being a "direct" descendant of George Washington are dubious, being a "relative" in some form isn't too far fetched.
Keep in mind that there really weren't that many people around back then, and if some members of your family date back to those times the possibility of being related to someone of stature is pretty good. Everyone that runs the Boston Marathon will be running near what used to be my 8th great grandfather's place in Framingham. Since he was the only one there at the time, odds are good he married Anna Rogers because she was one of the few available spouses in Cambridge, and there weren't many families named Stone or Rogers in the area that weren't related. So if someone is named Stone or Rogers and their family used to be in Massachusetts odds are good we're related. They had 11 kids, so you take that through 7 more generations you have some big numbers.
Same deal with the OP's roommate. If his family was around in Virginia during colonial times there was pretty slim pickings, and while George and Martha didn't have any kids George had 3 brothers, 2 sisters, 3 half brothers and 1 half sister. Ancestry.com figured there were at least 8000 descendants of George's father.
http://www.archives.com/genealogy/president-washington.html
Turns out that since my mom's family goes back to early North Carolina, and there wasn't many folks around here back there I have dozens of distant relations here in Winston-Salem one of whom I'm on the same master's swim team with. Seems like long odds that a guy from Minnesota would end up in North Carolina on the same team with a relative, but you do the math over several generations it's not so far fetched, so the OP's terminology may be off and he may be a relative or a direct decedent of one of George's brothers. Hopefully that little tidbit got him laid.
Turns out members of my mom's family, my dad's family, AND my wife's family all lived in Stuebenville, Ohio at some point. Not sure I want to see how the math on that works out.