That's partially true. In the early 2000's they were phasing out building their own transmissions (excluding the DSG)... After the disaster that the 4spd 01M transaxle was, the 09a was a Jatco transaxle that was also used in some Toyotas. Shortly after they started going with ZF autos, that were also shared with other cars.
I just changed the transmission in my neighbor's 05 passat diesel, and ironically the transmission is shared with several Bmw's. Even newer vw's several use ZF's. The one in my audi (zf8) is also used in dodges, bmw's, alfa romero's, jeeps, 5th gen supra, jaguars, Aston Martin... Pretty nutty the utilization of ZF's