After discussing this question with Shaykh Muhammad Al-Saalih Al-‘Uthaymeen, we came up with the following:
What we understand from the question is that the amount of money paid for the insurance is related to the value of the car, i.e. what the car is worth when the insurance is taken out. What this person is planning to do is a kind of lying, but it is done for the purpose of reducing the unfairness to which he is being subjected, namely being compelled to take out Haraam insurance. If there is no harm caused to him or to the reputation of the Muslims by his doing this, then there is no sin on him if he does that because he is forced to. And Allaah knows best.