This is only true if the power to run the electric car is environmentally less damaging than the diesel's emissions. With Germany's obsession with using diesel vehicles to mine brown coal to burn for power, I'm not convinced it is.
I think this is going to be very country specific. The UK for example has barely used any coal (relatively) for the main grid with a considerable amount of coal-free days in the past couple of years. (currently coal provides 0.0% of the UK's fossil fuel electricity production and nearly 14% is renewable[0] though it was up to nearly 3% in February[1]) So while there is still a majority of the electricity coming from fossil sources (namely gas) it is on the decline and I'd certainly posit that a somewhat modern power station can generate electricity more efficiently than a car's diesel engine can... (happy to be proven wrong on this as I can't find any direct studies)
