The lack of vehicle information in the LCM will be of little interest to insurers UNLESS the accident *may* involve lack of lighting, incorrect lighting or similar, which is when they will look into the vehicle lighting system and deduce that the LCM is not 'correct' for the car and as such could use that to refuse any claim or the third party insurer to put the blame onto the vehicle with the 'incorrect' LCM - who's to say the vehicle exterior lighting was working correctly, they could argue that it wasn't the right one for the vehicle and as such some of the exterior lighting was not working correctly to warn others of the hazard or driver intention.
If the replacement LCM had a higher mileage stored, they could also use this higher mileage as a basis for correct market value calculations when deciding on payout.....who is to say the BCU and the Instrument Pack are showing an 'incorrect' lower mileage and the vehicle is indeed higher mileage as per the LCM - they could use that as a loophole too.
But that is purely speculation......but if the accident were to do with a situation involving lighting, be it lack of signalling at a junction, or lack of tail lights, brakes lights etc...they *may* just use the fact the LCM is 'incorrect' for the vehicle as a get out clause.
Remember, regardless of if it has an MOT (which checks the function of the lights) and it passed the tests, that just means that the lights worked on the day of the test and would have no bearing on a claim that would be subsequent to that MOT test, they would still be checking that the lighting system of the car was correct at the time of the accident, not at the time of the MOT!