There could be multiple issues here.
1. Was it a domestic VOZ or international? Domestic we pass on instructions to the driver. Internationally it's direct to the driver.
2. How congested was the SMC frequency for the JQ crew to call 'holding short' of the bay? I've had numerous occasions in MEL where I can't get a word in to request taxi (or advise holding short) due to SMC also reading our an airways clearance and so on. It would indeed be a tragedy if this prang was contributed to by lack of ATCOs.
3.Agree with EWL about having your own staff with a perception of having their own 'skin' in the game (or at least the metal owned by 'their' employer). I'd be very interested to see how the training of the pushbackers at VOZ and other sub contracting companies compares with legacy training. Same? Different? Longer? Shorter? HF issues covered? etc.