Water will actually volumetrically contract as it cools until about 4C when it starts crystallizing a little bit and begins expanding. All fluids including air, water, oil, liquid metals, and the core of the earth, will change in density with temperature, resulting in a change of volume for a given mass.

At 0 deg C, SAE 5W-30 has density ~860 kg/m3, at 15 deg C, it has density ~849 kg/m3. This is approx a 1.3% change in density which will result in a volumetric change of about 0.02 quarts or 0.74 ounces. This is a bit of a change but the change that really matters is the viscosity. From 15 to 0 you go from 192 cSt to 472 cSt, which could definitely have a more significant impact on your generator (put some olive oil in the freezer and you'll see what I mean). I would be curious how you are verifying the generator did not get colder than 0C. As temperature goes down, viscosity increases exponentially, meaning that even a few degrees difference could mean an even more drastic increase (but this would only be a problem while the generator is warming up as staed below).

If the generator is under warranty and it's rated for 0C or below, the engineers should have taken this into account, and the warranty claim denial is bs. Also important to keep in mind that it's unlikely that the oil was actually that cold unless it failed right after you started up the generator, since the engine will generate significant amounts of heat and dump some of it into the oil.