Why It's Bullshit:
As you can probably imagine, when news of Sputnik 1 circling the cosmos reached President Eisenhower, he completely s**t his pants ... if, by "s**t his pants," you mean "breathed a contented sigh of relief." Oh, sure, the public freaked out about the commies taking over space, but as far as the U.S. government went, well, the Soviets were doing exactly what they wanted them to do.
See, prior to the launch of the Soviets' Sputnik program, Eisenhower's inner circle was more concerned with the legalities of space than with the technicalities of how to get there. Thanks to America's crack team of rocketry geniuses (aka former Nazis), the U.S. could have beaten Sputnik by a good year if it hadn't been for our legal worries -- namely, borders that, at the time, were considered to extend upward to infinity and beyond. So, by launching an object into orbit, other nations could potentially protest the U.S.'s illegal violation of their airspace every time it buzzed by overhead. But, by lobbing one tiny, metal beach ball into space, the USSR had just sent those concerns up in rocket smoke by setting a precedent. They paved the road for everyone else, thanks to the Russians' innate talent for not giving a s**t.
"We are over the White House. Release the communism."