B757 DURING PUSHBACK; AND DC9 TAXIING TO GATE; IN A CONFLICTING SIT.

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WE WERE PARKED AT GATE A AT LGA ARPT. ALL DOORS WERE CLOSED AND WE WERE READY TO PUSH BACK. I CONTACTED RAMP CTL FOR PUSHBACK CLRNC. HE INSTRUCTED US TO CONTACT GND CTL FOR PUSH TO SPOT ON TXWY M. I CONTACTED GND CTL AND THEY INSTRUCTED US TO 'ALLOW OUR COMPANY DC9 TO CLR US; PARKING ON GATE A;' THEN CLRED TO PUSH TO SPOT ON TXWY M. THE CAPT INSTRUCTED OUR TUG DRIVER TO 'PUSH AFTER OUR COMPANY DC9 CLRS PARKING ON GATE B REPEATING VERBATIM TO THE TUG DRIVER THE INSTRUCTIONS GIVEN BY GND CTL. THE TUG DRIVER SAID HE SAW THE DC9 BEHIND US. IT WAS CLR OF US AND PROCEEDED TO PUSH US. ONCE WE HAD VISUAL WITH THE DC9 WE REALIZED IT WAS STILL ON TXWY N AT ABOUT THE INTXN OF TXWY A PROCEEDING TOWARD THE GATE. THE DC9 SLOWED ITS TAXI AND OUR TUG PUSHED US TO SPOT WELL CLR OF THE ALLEYWAY THE DC9 WAS ENTERING. THE DC9 NEVER CAME TO A STOP AND THE PATH TO ITS GATE WAS CLR; SO THEY CAME TO GATE B UNINTERCEPTED. HOWEVER; GND CTL APPARENTLY HAD INTENDED FOR US TO WAIT UNTIL THE DC9 WAS AT GATE B BEFORE WE PUSHED. THE GND CTLR GOT UPSET ABOUT THE SIT AND STARTED TO BLAME THE RAMP FOR CLRING US OUT TO OUR SPOT. THE CTLR ASKED US WHO HE COULD OR SHOULD CALL ABOUT THE INCIDENT. IN OTHER WORDS; HE WANTED TO CALL WHOEVER WAS RESPONSIBLE FOR OUR PUSHING WHEN WE DID. WE TOLD HIM TO CALL OUR LGA OPS BECAUSE WE FELT THAT OUR TUG DRIVER HAD MADE THE DECISION TO PUSH US WHEN HE DID. WE COULD NOT SEE WHERE THE DC9 WAS SINCE IT WAS DIRECTLY BEHIND US. OUR ACFT NEVER CAME CLOSE TO DC9 AT ANY TIME NOR DID OUR PUSHBACK HINDER THE DC9 TAXI IN ANY WAY. THE CTLR INDICATED HE WAS GOING TO FILL OUT A RPT ON THIS SIT. IN MY OPINION OUR PUSHBACK OP IN NO WAY JEOPARDIZED THE SAFETY OF ANY ACFT NOR DID IT HINDER THE FLOW OF TFC AT LGA.