If the analog front end does not have high input resistamce then the current flow into it will cause a line voltage drop in the field wiring and transducer output amplifier. If hum or noise or RFI is what you wish to eliminate, better use filters, more controlled and definitely more predictable AC behaviour.
I was not worried about the DMM. A common DMM does not measure impedance only resistance, that too only upto the lower meg range and using low driving voltage. So even if you get high resistance between the 2 grounds, in poorly designed mains operated transducer the capacitive coupling/leaky insulation can cause enough problems if not smoke/failure when connected to the control system.