I don't know of anyone who has liability insurance and I don't know of anyone who changes their auto insurance to business use of the vehicle. You can, of course, be sued by anyone about anything any time and shopping is no different than any other activity. Your retirement nest egg could, in theory, be jeopardized by lawsuits based on 'psychiatric injury' due to a fender bender in the grocery store parking lot when you were there on your own to buy a loaf of bread and THEY ran into YOU.
I know of several shoppers who have been called in to testify in loss-of-job actions, but they have been called in by the defense rather than the prosecution. They suffered no personal loss except for time wasted. You are asked to report on your visit and as long as you do so honestly and objectively, I would have little concern. But possible ramifications are a reason I tend not to do 'Integrity' shops except with companies I feel will stand with their shoppers in the event that the client fires the employee and the employee sues. And standing with shoppers is why it is important to read the tenor and tone of your ICAs in addition to the words. A company that indicates they will sue the shopper if they are sued with the shopper required to bear the burden of all legal costs is NOT something I will agree to.