We'll technically they don't have to prove anything, you do.
If you tell them it's done 10k miles and then you have an accident a week later and it's done 16k miles you're hooped, and every year they will ask you at renewal, and if you've gone over your limit for that period you might get charged a premium, so it's always in your best interests to be honest, you're the only one losing out if you arent honest at the end of the day.
I'm with greenlight but I'm going to change soon.