Not related to the 370Z but I took my previous car to Progressive Insurance for body work and it had 1/2 a tank of gas. When I went to pick it up the Low Fuel Light was on I couldn't see 1/32th of a tank gas. No telling if any damage was done to the fuel system as a whole but I learned my lesson...people just cheap.
My 2c if you take your 370z in for any repairs leave it with a Full tank of gas and write down the miles on the OD.