.In general terms does anyone know if it is 'allowed' to cross over into Poland with a German hire car?
Only unless it's allowed by the particular car hire service. You need to check with them.
This was in around 1995 or thenabouts, but renting a car and driving ought to be no different in procedure.
The problem is that the insurance with hire cars doesn't always allow it.
In a worst case scenario the driver could be accused of car theft.