CE560 Captain reports being cleared direct GAI then adjusting heading slightly to enter a base turn for Runway 34. This turn is questioned by PCT; the reporter is told to proceed direct to the geographical center of the airport.

Narrative

We were cleared direct BAL direct GAI; before reaching BAL we were re-cleared direct GAI expect the visual. We were on autopilot heading mode and swung the heading bug toward the airport. Approximately 12 miles from GAI we had the field insight and I entered a waypoint for a 2 mile base for the runway in use. My First Officer who was flying made a small turn less then 10 degrees in the direction of the fix while I waited to contact ATC who was busy talking to another aircraft; to tell him we had the field insight and could accept the visual. When he finished with the other aircraft he immediately asked our heading; and I replied with our heading. He asked if we were tracking for the airport and I said we were heading for a base to 34. He was irritated and said he needed us to track to the geographical center of the airport and we made an immediate turn toward airport center; he then added; it wasn't bothering him but it was making other people nervous we were drifting toward Washington airspace. I apologized for any misunderstanding and the subsequent approach and landing was uneventful. After doing more research I still have not come up with an answer if we did anything wrong. I know we were cleared direct to GAI but its always been my understanding that as long as we were approaching at an angle to intercept the airport traffic area we were headed directly toward the field; even our SOP's have us enter the runway of intended landing into the FMS before entering the approach environment; which can be several miles from the geographical center of the airport. I would appreciate any insight into this manner.