Pilot reported confusion regarding the location of an entry/exit gate within the Washington D.C. FRZ after ATC indicated the pilot was too far off the correct route to exit through the planned gate.

Narrative

I was conducting a VFR flight from VKX to ZZZ in the DC FRZ (Flight Restricted Zone) on an approved flight plan. I requested from PCT and was cleared to transit the ADW Class B airspace. I proceeded eastbound to exit the FRZ south of the DCA123 radial as required. The PCT Controller (I believe 125.62) issued two vectors; to a heading of 090 then 100; then slightly scolded us to review the DC SFRA NOTAM because we were too far north for the gate. This was confusing because we were south of the DCA123 radial as required for the VKX gate. I then queried the Controller if the radial had changed and he stated that he did not know; but if we had the fix identified we could resume own navigation and miss it. I do not believe any airspace violation occurred; I believe the Controller was just looking out for us; we were not issued a Brasher warning or any follow up. As a former Controller; I am writing this report because I wonder if the FRZ gates may not be published correctly on the PCT radar scopes. Perhaps it is as simple as the Controller was working several sectors and zoomed out to a point where it looked too close while eyeballing the situation. I believe the FRZ gates should be published visually on the sectional and TAC charts to assist in identification. The Controller was also unable to verify when I asked if the DCA123 radial was the correct limit of the gate; the FRZ map in STARS at PCT should be updated to contain that radial name for quick reference by Controllers attempting to assist pilots.