If we define the Space Race as starting in 1955, which is when both the US and the USSR declared they'll get a satellite into orbit, this statement is completely and categorically false. Though I am unsure of the degree of German involvement in the US space program, there was absolutely no German participation in the Soviet program from 1951 on. Pre-1951 German role in the USSR was limited to consulting and technical training, so we can safely say that German influence on the Soviet space program was limited. The USSR had enough internal talent anyway; Korolev (R-7, Vostok, Luna), Glushko (the vast majority of the Soviet engines) and Chelomey (Proton, various ICBMs and military rockets) were more than a match for Von Braun and his crew.