^what the others have said. Let your insurance handle it. Worst case is you pay a deductible (depending on your coverage) and when your ins collects from the other company you get the deductible back.
Have no idea on the diminished value crap. That sounds like it would only apply for totaled cars. Yours has an estimated repair cost to make it just like it was and if the body shop needs more they go back and get it.