Andy could be wrong, since:
BLACK BOX
/
+-------------------------+
| |
| +-------+------+ |
| | | | |
| | [R1] [R3] |
| | | | |
| | | +----------->E1
| [SUPPLY] | | |
| | +------|----------->E2
| | | | |
| | [R2] [R4] |
| | | | |
| +-------+------+ |
| |
+-------------------------+
as long as R1/R2 = R3/R4, then E1 will always equal E2 even though the two wires aren't galvanically isolated.
However, since an ohmmeter is a voltage - or current - source, once connected across E1 and E2 it would unbalance the bridge, causing charge to flow, and it would indicate some resistance.


In the attached images, the fixed resistors in the bridge - the ones in the gold anodized housings - are 120 ohm 3% wirewounds.
The ones on the right are in series, with about 25V of excitation across them from the little HP6216 on top of the decade resistor box, and the one on the left is in series with the decade resistor box and a 50 ohm pot used to balance the bridge with the same excitation supply across that string.
The best I could do was to balance the bridge to 3.1 millivolts on its output, as shown on the Fluke, and the Wavetek was set to 200 ohms, and wasn't connected to anything.
In the second image, the ohmmeter was connected across the output of the bridge and, as you can see, the bridge was unbalanced by about 106 millivolts and the ohmmeter read 116.1 ohms