The fear of accidents is certainly understandable. But if you dissect that fear, it tends to come from fear of personal (or your family's) bodily harm, financial burden and headache and possibly liability, and probably lastly, causing harm to others.
If an accident is merely an inconvenience that you walk away from and hail another Robo, in which nobody is seriously harmed because of the system's ability to at least reduce collision severity, and from which you have no resulting headaches to deal with it (insurance, repair, etc.)...it kind of becomes less frightening.
"Yeah my Robo hit another car on the way to work. Sorry I'm 10 minutes late..."