I'd say the Soviets absolutely shot down that U2 in large part to prove that they could, and that to some degree at least, the US was flying those planes over to prove that they could.

There's a school of thought that says the US won the cold war by convincing the Soviets to bankrupt themselves trying to keep up with the arms race. Now I don't necessarily think that fully explains things, but I do think there's a lot more politics to a "spy" device than the actual photographs, especially outside the context of a hot war.