Would she veto you using a car if you were in a fender bender?
The reality is that pretty much everything we do comes with some degree of risk. I'm a paramedic and I've seen serious injuries to cyclists, pedestrians, and drivers. I've also seen serious injuries from falling down steps, mowing the lawn, woodworking, playing baseball, slipping on the ice, falling out of bed (no kidding), putting up Christmas decorations, cutting firewood, riding horses, boating, kitchen appliances, etc . . . and so forth . . . and you get the picture. You can determine how dangerous your cycling will be by the precautions you take and the manner in which you ride. Thank your wife for her concern, but point out that your good riding habits may have turned a potentially serious situation into a minor incident.
For some reason, cycling is viewed differently than other activities that involve risk. I've never quite understood why when a drunk driver wipes out another driver, they blame the drunk, but when a drunk driver hits a cyclist, somehow it's the bike that's dangerous.