Can only speak for MAN but I find this surprising.
We often pushback aircraft on adjacent stands side by side without a problem.
There is the chance of a jet blast problem if one taxies away from the other at more than minimum power, whilst the pushback crew are still at the other aircraft.
This "safety" reply is probably a knee-jerk reaction to an incident. We have to tell aircraft that are taxying off stand to use minimum power due to a previous incident.
On a related note - if you've not got direct verbal commms with your pushback crew (a requirement @ MAN) tell us BEFORE you accept a conditional or non-standard pushback.