Car insurance claim but no MOT?

my partner had a crash today and it was totally the other persons fault as my parter was indicating to turn right and some idiot tried to overtake him on the right , hitting his side. the police said not probs its totally the other persons fault and we claim off his insurance not ours but when the police checked the car they discoved the mot ran out a month ago, my partner explained we though we had updated it and they were fine about , prob believed us as we had tax and insurance, they dont worry just tell your insurance about the crash. i know car insurance is not vaild but surely its okay if its only the other person paying out? car in the garage and does not seem to be any probs so far......do you think we will be ok, it really was a genuine over sight