In a word- - - -NO! The gasoline is getting into the crankcase from a hole in the fuel pump diaphragm, or a carburetor that's flooding severely and filling the intake with gas, which then finds its way past the rings when the engine stops.
Severe flooding can wash the cylinders down, resulting in poor ring sealing, but once the source of the gas-contaminated oil is eliminated, it shouldn't be necessary to change the rings, unless they're worn out anyway. If the carbon deposits behind the rings on a old engine get washed out by gas-contaminated oil, the compression can drop severely because the carbon was the only thing keeping the rings in contact with the cylinder walls.
Find the source of the gas, which will probably be the fuel pump, then fix it, change the oil, and run a compression test. Anything around 85 pounds or more, up to maybe 100 PSI, will mean the rings are probably OK.
Jerry
