COMMUTER TAXIES WITH PERMISSION ONTO RAMP AREA IN FRONT OF 767 WITH MECHANICAL.

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WE WERE TAXIING INBOUND TO GATE X IN LGA FOLLOWING INSTRUCTIONS FROM GND CTL. WE WERE ON INNER TXWY; HOLDING SHORT OF XRAY. AN ACR 767 PUSHED BACK FROM GATE Y AND WAS BLOCKING THE ALLEY WAY. HE APPARENTLY HAD A PROB WITH THE TOW BAR AND ASKED FOR MECHANICAL ASSISTANCE FROM ACR OPS. IT WAS APPARENT THAT THE 767 WAS NOT GOING TO MOVE FOR SOME TIME. WE CALLED ACR OPS TO ASK FOR CLRNC INBOUND WITH THE 767 IN HIS PRESENT POS. I CONSIDERED THE 767 TO BE IN THE ALLEY WITH A MECHANICAL RATHER THAN AN ACFT ON PUSHBACK. ACR OPS SAID WE COULD TAXI THROUGH GATE Y TO GET TO GATE X AS LONG AS WE HAD WING WALKERS ON BOTH SIDES. WE REQUESTED ADDITIONAL WING WALKERS FROM OUR OPS AND ANOTHER AGENT CAME OUT TO DIRECT US IN. WITH 2 WING WALKERS AND A MARSHALLER; WE SLOWLY PROCEEDED IN FRONT OF THE DISABLED 767. WHEN WE WERE DIRECTLY IN FRONT OF THE OTHER ACFT; AN ACR RAMP AGENT ON A TUG DROVE BTWN MY ACFT AND MY WING WALKER ON MY L SIDE. BOTH HE AND HIS LEAD AGENT WERE VISIBLY UPSET AT THE FACT THAT WE HAD OUR ACFT WHERE IT WAS AND THEY CONFRONTED OUR RAMP AGENTS AFTER WE WERE PARKED. BY THE TIME ALL OUR PAX WERE OFF OUR ACFT; NO ACR RAMP PERSONNEL WERE AROUND. AFTER DISCUSSING THE INCIDENT WITH OUR LEAD RAMP AGENT AND AN AGENT WITH ACR OVER THE PHONE; THE SIT WAS RESOLVED. A COMBINATION OF MY IMPATIENCE IN GETTING PARKED AND THE ACR AGENTS INATTN CONTRIBUTED TO THE NEAR INCIDENT. ALL PEOPLE SHOULD KNOW NOT TO DRIVE IN FRONT OF A MOVING ACFT; EVEN IF THE ACFT IS IN A POS IT IS NOT EXPECTED TO BE IN. IF I AM FACED WITH ANOTHER SIMILAR SIT; I WILL JUST WAIT UNTIL THE ALLEY WAY IS COMPLETELY CLR REGARDLESS OF OUR CLRNC INBOUND AND DIRECTION OF OUR RAMP AGENTS.