You got it the other way round. While you are correct on the accuracy part, we are not worrying about exactly how many volts in this case, but about if the measured voltage is a phantom/capacitive coupling effects created voltage to ground or not. So you need a meter with low impedance, such as an analog meter with the low range selected. Think "potential divider"..
So agin, he needs to get a meter with low input impedance, such as an old analog meter and set it to the low range. A digital multi-meter that he was likely using would likely have the typical 10 MOhm or higher impedance. While such high impedance does result in accurate voltage measurements as you said, it is not suitable for use to determine if the voltage is just created by capacitive coupling effect.
As a matter of fact, I could get as much as 50 V ac on my Marantz AV8801 (I was surprised too as I expected only a few volts due to the commonly found capacitive effects on the so called "double insulated" , i.e. ungrounde scheme. Then I pulled out my old analog multimeter and it registered the expected low voltage, about 1-1.5 V at the 25 V range and about 40 V on the 500 V range when the impedance would be 2 MOhm, still lower than digital meter's typical 10M Ohm or higher.
I think @Speedskater
knows what I am talking about, surely you do too, but you are thinking in terms of accuracy.