Except that's absolutely not true in any sense, as we've established in this thread... you don't claim on your insurance if you're not at fault. Insurance covers vehicles without MOT so long as the incident wasn't caused by an issue stopping the car being roadworthy. MOT and insurers have literally no relation, MOT is proof of roadworthyness and insurance is a policy with a company to cover costs of at-fault and non-fault accidents, assuming the car is roadworthy. Even if it isn't road worthy, like the lights don't cast a correct beam pattern, if you crash in daylight then why should it be considered? If your car isn't roadworthy because it's brakes don't work and you rear end someone, then yeah, insurance isn't going to pay out.
Will leave it there as feels like this is going in circles a bit!