You are correct, Bloo. Chrysler used the most confusing nomenclature possible for its transmission choices in the late 40's/early 50's. Many people understandably misuse the name "Fluid Drive" to refer to the transmission. As you say, "Fluid Drive" actually just referred to the fluid coupling between the engine and transmission. Almost all the cars (and definitely all the Chryslers) had the M6 semi-automatic transmission, which was called different names depending on the make ("Presto-Matic," "Gyro-Matic," "Tip-Toe Shift"). But some cars had a regular 3-speed transmission behind the fluid coupling.
This seems like a very nice car, but I agree that the transmission issue, whether "minor" or not, should be repaired by the seller before the car is put on the market.