The Buick Dynaflow and Chevrolet PowerGlide were completely different transmissions than the GM Hydramatic. The Hydramatic was, at that time, a 4 speed unit with a fluid coupling between the engine and the transmission. The Dynaflow and the PowerGlide had a torque converter between the engine and the transmission. The Dynaflow depended on torque multiplication rather than gears as did the Chevrolet PowerGlide until 1953. In 1953, the PowerGlide became a 2 speed unit that would start in low and shift to direct drive when the selector was placed in drive. If you wanted to start a Buick Dynaflow or a 1950-52 PowerGlide Chevrolet in low range, you had to manually select Low.
As I said in my quote, not being able to pushstart the Hydramatic happened in 1959. The cars equipped with this transmission in the GM line were only the Pontiac, Oldsmobile and Cadillac. In 1961, the Hydramtic was changed for some models and became a 3 speed unit that was called the “SlimJim”. It had a torque converter. I don’t know if GM cars equipped with this transmission could be push started or not. Interestingly, the Pontiac Catalina had this “SlimJim” transmission, while the upper Pontiac lines (Star Chief and Bonneville) had the older 4 speed GM Hydramatic.
To confuse the issue even further, in the Ford line, Ford and Mercury introduced an automatic transmission in 1951 that was made by Borg Warner. However, the Lincoln in mid-1949 introduced the Hydramatic transmisson made by GM. I’m not certain when Lincoln stopped buying its automatic transmissions from GM, but I think it was after 1953. The point is that automatic transmissions are different.
One more little interesting note: The GM Hydramatic plant suffered a disaterous fire in 1953. Some Pontiacs were equipped with the Chevrolet PowerGlide. The PowerGlide did have a “park” position on the shift quadrant–the GM Hydramatic did not. My uncle had a 1953 Pontiac that had the Chevrolet PowerGlide transmission. I believe that some Oldsmobiles may have been equipped with the Buick Dynaflow, but I’m not certain about that.