That's interesting, and I don't doubt your claim (!) about the insurance issue in your airline, but certainly in our airline this is not the case. We always used to use the line 'you will not be insured' if a pax were to get up when the FSB was switched on but when HQ heard we were saying this, they said that tgis was not true. What is true is that they will not have a leg to stand on (quite literally, in some cases!) if they were to try and sue.
Yes, effectively the same thing - you have a claim on the airline if injured while abiding by the rules, which comes off the airline insurance policy; if disobeying the rules the insurance policy does not cover the injury and the airline is not liable for any claim. Same as the insurance; just that the insurer pays for successful, legal claims.
I work in financial markets, not airlines, hence my insurance know-how.