A319 Captain reported on pushback; aircraft wing encroached upon taxiway resulted in a evasive action and a critical ground conflict. Captain also reported that ATC stated that a collision is not possible from that gate; yet ground crews state that ATC is not allowed to clear traffic on that taxiway when pushing from this gate.

Narrative

After getting clearance from Ramp Control and checking in with Ground Metering; we were given clearance by the ZZZ Ground Controller on XXX.X to pushback from gate XX; tail east and not to block Taxiway 1. I communicated this to the tug driver. During the pushback; we needed to encroach onto 1 in order to put the plane's tail into the alley. At approximately XA:25; an RJ was taxiing; at a fairly rapid rate; southeast-bound on 1 and the astute wing walker on the aircraft's left side signaled to stop the pushback. The tug driver stated that it would have been a collision if we had kept going. I advised the Ground Controller of this and was told in no uncertain terms that there was no way that a collision could have happened. I replied that our wing was protruding well into Taxiway 1; near the painted centerline. The Ground Controller then stated that he had been doing this sixteen years and it never would have happened.The First Officer; myself; and at least two of the three ground personnel heartily disagreed with that sentiment; hence the reason for this report. We do believe that a collision definitely would have happened had the tug driver not stopped the aircraft in time.The tug driver then informed me that Ground Control was not supposed to allow an aircraft to taxi onto 1 when one is pushing off of [gate] XY or XX. I would like to commend the wing walker who was paying attention and noticed this in time; since the tug driver could not see the aircraft approaching from behind him.Cause: Ground Control cleared an aircraft to taxi onto 1 at the same time we were encroaching onto 1 during our pushback.Recommendations- don't allow these two events simultaneously