If that was literally their job that they are being paid to do and you were specifically using the gun to film a movie involving you pointing that gun at someone and pulling the trigger under the pretense it was cleared and verified by a professional prior to the filming, they should definitely shoulder some burden.
Arguments can be made about working conditions not being suitable causing mistakes to be made and those conditions were brought on by Baldwin, but then he should be treated almost as two separate people. If it had been a different actor to pull the trigger, would that actor be liable? Would the producer, or whatever role Baldwin had outside of acting, be liable?