I am always personally insured, and most all of the jobs I have completed, did not require coverage and liability for public or other's personal belongings. The only kind of jobs I did that required extra saftey and health measures for not only myself, but for others who may be nearby, were the jobs that required excessive amounts of paint spray using the spray gun to paint large areas on large murals.
I ALWAYS took extra precaution to protect those around the painted area inside buildings, including surrounding cars or buildings nearby; I achieved this by using plastic tarp to close off areas being painted, while using proper ventilation in opposite directions while wearing proper respiratory equipment and eye protection.
I also created at least 10 - 20 foot barriers bewteen the area being painted and around it, by adding caution tape held up by portable poles / stands just to keep others at a distance. I have never had any problems or complaints using those procedures either.