Maybe they were running an escort with a VIP Military plane. Could be, but wouldn't you think they'd have been with that VIP plane all along, instead of just catching up with it?
Could also be a whole squadron transfering somewhere else with support crew and maintanence in a larger aircraft.
We have an airfield at Fort Belvoir. During time of war it has a lot of traffic. They have another one further South at Quantico. Then, there's another one even further South.
Not everything going on has to do with Andrews AFB or DCA.