Although the Soviets had a very similar system (Operation Osoaviakhim) to get German scientists after the war, although less well known (and also a bit less voluntary on the part of the scientists)
Meanwhile the "American Germans" were welcomed, decided to make the US their new home and contributed heavily to the US space programme.
In the US the germans could build the rocket program by their own without much US interference, until Lyndon Johnson broke it up.