Oh, but come on, we're talking hundreds of light-years. The ship would've had to be near the edge to begin with in order to get blown across it. Again, you're missing the point, which is that if it were that easy for a more primitive ship 200 years earlier to get to the edge, then it doesn't make sense that nobody else got there before the Enterprise. The question is not just how the Valiant got there; the question is, if they got there so long before, why did nobody else?
I figure the "storm" was one of those anomalies made famous by later Treks and it took the Valiant sectors way from its original position.
As to why other species' ships haven't ventured out of the Galaxy...( waves hand) these aren't the droids you're looking for