Basically, the receiver is a 'floating' resistor across the input to a differential amplifier. The resistor generates a voltage proportional to the 4-20mA current. Whether the low side of the resistor is grounded or not makes no difference to the diff-amp (as long as common-mode voltages aren't exceeded) If you're using a ground-referenced current signal from the transmitter, you have to ground the low side of your input (to complete the loop). If it's a two-wire transmitter, don't ground the low side.
My guess is that a transmitter that generates its own current will not work when connected to an external power supply and could possibly be damaged. Basically you would be connecting an output to a power supply. But you need to look at the specs for the specific transmitter.