This type has an extra identification light, about the size of a landing light. It is mounted on the left side of the nose, pointing left slightly fwd and slightly up. The light allows the F-16 pilot to intercept another aircraft and slide in behind and low, out of veiw from the other pilot. The F-16 pilot then turns on the ID light and can get a good look at the tail markings and numbers of the intercepted aircraft.
You probably did see an intercept as the Washington area is a very high security area under constant airborn CAP. Aircraft are intercepted and identified on a routine basis. You probably saw the ID light reflected off the intercepted aircrafts' tail.
Now that's an interesting idea, and quite possible. My recollection is that it looked like a bright light shining in my general direction, but it could also have been glare or a lit-up part of the airliner.