Those "Completely American" Marxists often had quite close ties to, or were part of, the "Comintern" (Communist International", the "evangelical" extension of the Communist Part of the Soviet Union.
The Comintern (Communist International -[actually the 3rd]) was set up in by Lenin in 1919. It was to be a co-ordinating body for the communist parties. Membership required, originally, agreement on 21 points set by Lenin. Moscow's demands for agreement on all its points caused immediate splits, among the "International" (like the French), and in time, under Stalin, led to its dissolution. It originally included primarily four groups of U.S. Marxists; the Socialist Labor Party, the Socialist Party of America, the trade unions IWW and the Workers International Trade Union. You can read their histories and relationship (or not) to the Comintern here: http://en.wikipedia.org/wiki/Comintern
You can read from their histories that they were far from a monolithic group. The original Comintern was dissolved in 1943, with its greatest influence over the largest US groups excercised by that time. It was succeeded in 1947 with the Cominform, which itself was dissolved in 1956 in the process of De-Stalinization. During Stalin's leadership various factions split over the issue of following his lead or not. The founders of International A.N.S.W.E.R. were diehard Bolsheviks who left the CPUSA when it left the Comintern over Stalin and they did not want to.
The collective history of the various US communist factions indicates that control and/or influence of the US groups by the Comintern declined over time and had little direct control by the late 1950s. That is not to say that the KGB did not continue to exploit their fraternal party relationships to obtain US national as well as US political intelligence, on democratic as well as communist parties.