Book value on an LS in good condition seems to be about $3000-$3300, which comes closer to $4k. Especially if you can part out the totaled car after buying it back.

When my car was totaled, I got book value, which was a few grand greater than the purchase price, less $250 for scrap value of the car. Plus a 10-day rental voucher. So this works both ways.

Insurance companies tend to go by book rather than purchase price, since making an aggrieved party whole means giving them the actual value of a destroyed item. Whether book value = actual value is another open question 🙂