PA28 pilot on an SFRA flight plan reports being vectored toward the FRZ by PCT. With the boundary close; as shown by on board GPS; he attempts to turn away and so advises PCT. PCT advises to maintain assigned heading and that FRZ entry is permitted under PCT control.

Narrative

I was on a SFRA flight plan and my clearance in the Bravo airspace was from BRV gate Direct OTT direct PALEO. Just south of OTT I was give an assigned heading for traffic that pointed me toward the FRZ. After a short time on this heading I turned eastbound contrary to my assigned heading when my Garmin 430W and handheld GPS both showed me within a mile of the FRZ boundary. I advised ATC I was turning due to the FRZ he stated that 'I am providing Bravo services and as long as you are with me you are fine even if you go into the FRZ'. I advised him that I was uncomfortably close to boundary and he said he was showing me farther away then what my GPS was displaying. He advised me that he would provide on course shortly. I continue the assigned heading and then finally received an on course heading that brought me away from the FRZ. I know of no instance listed in the NOTAM for the SFRA/FRZ where ATC can clear a pilot or GA aircraft without a PIN and FRZ flight plan into the FRZ without a waiver from FAA/TSA. I was forced to deviate to remain clear of the FRZ and there was quite a difference in what the controllers radar was showing compared to my onboard WAAS GPS devices.