Building Officials are often statutorily protected under the government employee indemnity (with some exceptions).
Stand alone inspection services is a different issue. Architects and Engineers typically are NOT government employees when they engage services to the public. Architects & Engineers have professional liability NOT because of license but because they are commercially engaged in providing service(s) to people for remuneration. Drivers have insurance because they drive. Architects and Engineers have insurance to cover costs of errors and omissions because of decision in case of a lawsuit based on negligence/tort. Building Designers ALSO have liability and they do have insurance especially if they are designing non-prescriptively. In Oregon, I can face lawsuits of tort/negligence based on E&O and other Professional Liability when I am the designer of responsible charge.
If I was a consultant to an Architect, some indemnification would be in place because A) I am not engaging in practice of architecture and B) The Architect is by law the responsible party for practice of architecture and C) I won't engage in the practice of Architecture without an architect and D) I want no liability to the Architect's service and E) I want to protect myself because it is the Architect's responsibility to make sure the work is properly reviewed before he/she stamps the work and I'm not taking any share of liability even if it is in part my fault, the architect is suppose to catch it. Just like an employee.
However, when I design a building (under the exemptions) for a client, I have ultimate responsibility just like the Architect would. If you take charge, you have the responsibility of that charge. Simple.
Hence the saying - Architect/Engineer of Responsible Charge or in my case - Building Designer of Responsible Charge. It is legal theory by contractual law that the "Contractor" (generally not just Construction Contractor) assumes responsibility for the service the "Contractor" provides. Architects, Engineers and Building Designers are "Contractors" (ie. INDEPENDENT CONTRACTOR) not just Construction Contractors which is also commonly called Contractors for short.