Citation V/Ultra/Encore (C560)
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 50; Flight Crew Total 7760; Flight Crew Type 3700
ATC Issue All Types; Deviation - Track / Heading All Types
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Human Factors; ATC Equipment / Nav Facility / Buildings
We were cleared direct to FRISY the IAF to intercept the LOC to FLG. It was about a 030 heading. Our FMS showed that we were proceeding directly toward the fix. Shortly before the fix ATC asked if we were heading toward FRISY. We replied that we were. We were then told to turn right to a heading of 070 for vector to FRISY. We complied. We then were given a 170 (I am not 100% sure of the heading back to FRISY. We then were told to intercept the localizer. At some point in time the controller said that we had been correct in our original course to FRISY and that he had 2 overlays of the map.
CE560 Captain reported being cleared direct to FRISY then being issued a heading when ATC deemed the current heading to be incorrect. Later ATC issued a new vector to FRISY and advised that the original heading had been correct and that he erred due to two overlays on his scope.