I'm guessing that tread cut and the sidewall bulge are in close proximity to each other. If so, then the cut caused a belt edge separation, which is what the bulge is. It was not caused by running the tire flat!
Are you sure your wife hit something? Perhaps she just said that as in: "I don't know, honey, maybe I hit something, but I didn't see anything!".
The reason I ask is that the cut seems to have cracks at the end of the cut and that would have taken quite a while to develop. Plus, the bulge would be best explained if the cut had been there quite a while.
And was the tire actually run flat? It doesn't show any evidence of it.