AHN CTLR CHALLENGES PA28 PLT'S RPTING PROC WHEN CONDUCTING AN IFR APCH.

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CTR TURNED US (ACFT X) OVER TO THE TWR JUST OUTSIDE THE FAF. WHEN WE CHKED ON; THE TWR ASKED US TO RPT BULLDOG. I SAW THE ADF NEEDLE SWING AND SAID WE ARE AT BULLDOG NOW. CTR HAD CLRED US FOR THE RWY 27 LOW APCH; CIRCLE TO LAND RWY 9. WE CONTINUED THE APCH AND AT THE ARPT BOUNDARY WE WENT MISSED APCH AND RPTED IT. THE TWR CTLR SAID WE HAD NOT RPTED BULLDOG AND ANOTHER ACFT (ACFT Y) HAD TO TURN TO AVOID US. THE TWR CTLR SAID HE DIDN'T UNDERSTAND WE WERE AT BULLDOG AND SINCE HE DIDN'T ACKNOWLEDGE THE RPT; THE RPT WAS NOT VALID. HE THEN TOLD US TO PROCEED VFR TO GRD. WE ASKED FOR OUR FILED ALT AND REMINDED HIM WE WERE IFR. HE THEN GAVE US OUR FILED ALT OF 4000 FT AND TURNED US OVER TO ZTL. I TALKED TO THE CTLR WHEN ON THE GND IN GREENVILLE; SC; AND HE SEEMED TO THINK WE SHOULD HAVE RPTED BULLDOG AGAIN AND THAT WE WERE INCORRECT TO CONTINUE THE APCH THAT CTR HAD CLRED US FOR. IF HE IS CORRECT AND WE DON'T CONTINUE THE APCH; WHERE DO WE GO? MISSED APCH? HOLD? WHAT IF WE HAD ACTUALLY LOST RADIO CAPABILITY? I THINK HE SHOULD HAVE PROTECTED THE APCH AIRSPACE.