CL65 CREW GOT A GPWS TERRAIN WARNING WHEN THE APCH CTLR DSNDED THE ACFT TO 3000 FT VERSUS 4000 FT.

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NEAR FILPS INTXN; WE RECEIVED A RADAR VECTOR OF 170 DEGS TOWARD THE ILS RWY 9 FINAL APCH. FROM 6000 FT; WE WERE ISSUED A DSCNT TO 3000 FT (250 KTS/APPROX 1900 FPM). DURING THE DSCNT; WE HAD OCCASIONAL GND CONTACT; WHICH LATER SEEMED AS IF WE WERE GETTING CLOSER TO THE GND THAN NORMAL. A FEW SECONDS LATER; THE GPWS ISSUED A 'TERRAIN; TERRAIN' WARNING; TO WHICH I IMMEDIATELY EXECUTED THE APPROVED ESCAPE MANEUVER IN THE FLT STANDARDS MANUAL TO A LEVELOFF OF 4000 FT. AS I WAS DOING THIS; THE CTLR STATED THAT THE ALT SHOULD BE 4000 FT. NO OTHER CONFLICT RESULTED FROM THIS EVENT. MY CAPT AND I BOTH HEARD THE CLRNC TO DSND TO 3000 FT; WHICH WAS READ BACK PROPERLY WITH NO CORRECTIONS FROM THE CTLR. WE DIDN'T TAKE ISSUE WITH ATC AT ANY TIME. SUPPLEMENTAL INFO FROM ACN 617750: GOING INTO SWF; N90 APCH GAVE US A HDG OF 170 DEGS AND 6000 FT ON THE 170 DEG HDG. ATC TOLD US TO DSND AND MAINTAIN 3000 FT. I READ BACK 'DSND AND MAINTAIN 3000 FT.' (THERE WAS NO CORRECTION TO MY READBACK) 3000 FT WAS SET AND CONFIRMED AND MY FO BEGAN THE DSCNT. AT 4000 FT; WE CONFIRMED DSNDING FROM 4000 FT TO 3000 FT AND 1000 FT TO GO. AT APPROX 3450 FT; WE RECEIVED A GPWS 'TERRAIN.' THE ESCAPE MANEUVER WAS PERFORMED SIMULTANEOUSLY AS ATC CALLED AND STATED 'ACR X; YOU WERE CLRED TO 4000 FT.' WE LEVELED AT 4000 FT AND LANDED WITHOUT FURTHER INCIDENT.