a) If the landlord provides wiring that is/was to-code when installed.
b) If the code states that a refrigerator should be on a dedicated circuit.
c) If the tenant attempts to go around the original and proper installation and/or add additional load than just the refrigerator.

It is unlikely the landlord will get dinged 'if the building burns' - as the lawyers will go through the first-cause (you) first.

Line drop: is it 3 volts under load? Is it 3 volts in general? What gauge is the wire, and how long is the run? And are there any splices along that run? As an example, we have a 12-gauge, 20 A dedicated circuit to our refrigerator that is about 75' in developed length, no splices. Just for giggles, we have 118 V at the panel, line-to-ground, and 117 V at the receptacle, unloaded. And within the limits of measurement error anyway.

Peter Wieck
Melrose Park, PA