If they want to pay you that is fine since you know how much it is. No down payments and no paying it off. Since they sere nice enough to call you give them the option of paying before you file it against their insurance, which it sounds like they have. If they don't have insurance and won't pay, then turn it over to your insurance and let them deal with it. The first money they collect from them will go back to you for the deductible.

But the best option, easiest and best for all is for them to pay you for the damage and in cash or a good check. Congratulations it sounds like your were run into a kid with responsible parents. That is like having a unicorn poke you in the butt.