That's not correct at all. Lack of QI means the officer (in this case) is directly responsible in any ensuing civil suit. It doesn't mean the department can't also be sued, but lack of QI puts the officer squarely on the hook.
It is correct. All states in New England, which is all I've looked at so far, indemnify cops by statute.
Here's CT, NH, MA, ME, RI and VT. They all indemnify cops from civil liability unless the action was wanton, reckless, malicious, in bad faith, gross negligence, or some combination of those terms.
General Law - Part I, Title XVII, Chapter 120A, Section 7
malegislature.gov
Vermont Laws
legislature.vermont.gov