“While it was true that the Russians voluntarily gave up some territory in the 90’s”
Russia gave up its hold on all of pre-war Eastern Germany, Poland, Belarus, Czechoslovakia, Ukraine, Hungary, all of the Baltic states and the Balkan ones too. In other words the bulk of the European continent if you exclude western Russia itself. It was a combination of pressure at home and pressure from those countries, and finally open defiance from the populations of those countries that finally made the difference. The lead up had been simmering since protests began breaking out during the Afghan war in the 1980s.
None of it had anything to do with anything the USA was doing at the time. a few hundred thousand (at most) American troops in western Europe was completely irrelevant. It had never been more than a token anyway.
The line for the so called iron curtain was drawn up at Yalta and finalised at Potsdam and was agreed by the United States mostly because in 1945, the United States didn't have much choice. Stalin held all the cards. Nevertheless, Roosevelt and later Truman, agreed too. So it appears that until the 1990s anyway; the Russians managed to keep the Americans out of most of Europe, and not the other way around.