Yes, it's probably a worn or sticking carburetor float needle/seat that is flooding the engine internally with gas when it it shut down. This can occur regardless if the fuel is gravity fed or if the engine has a fuel pump. Most modern small engines on LGT's have an electric solenoid at the carb that shuts off the fuel flow to the carb when the ignition is off to prevent this, but I think that's after the time of the 2164.
The flooding gas works its way into the oil just as dqdave1 described.
-Fordlords-