Ambient radiation has its origins in previous nuclear warfare, and all societies that have spawned since have had the proper tolerance.
Maybe.
Maybe.
I love the idea, it's amazing to think about. And it might be true.
However, we can't prove it, we can't disprove it, and it has no bearing on our current state. In the absence of evidence I've got to try to apply Occam's Razor, so the simplest of competing theories should be selected as the one to go with until/unless evidence shows otherwise. Which means we should consider humans the first advanced civilization on Earth until other evidence is found.