Mythbusters used consumer model rocket motors ''not'' a ''large'' Jato unit / units.
The military used different size ''Jato'' units ''way'' back in the day,, ''size depending on application'', & development.
They also made a 67'' Impala station wagon, that had a ''huge'' long roof.
Plenty big for a ''Jato'' unit / units., like for B-50's & B-47 Bombers ect.,, which used them.
The story to me, is just ''way'' to detailed, to be just a myth.
Also think it's doable, if the car was doing around 100mph & then lighting it.
B-47 Jato take off, 1952.
Gross take off weight of this Bomber was 133,000 - 230,000 lbs., ''depending on landing gear strength''.
Gross weight of a 67' Impala wagon with say a ''possible/myth'' 427 option,, was probably around 8000 lbs.
Those were turbonique engines. They were quite powerful and had a bad tendency to explode. They sold a proprietary formula that included hydrazine and they were sued out of business and you would have to figure out how to make the fuel to use it for anything but a historical collectors item. Jack McClure went 215 in the quarter mile with one. Article here. the photos below I took at Don Gartlis museum.