Just out of curiousity, did you tighten the cap properly? or did you accidently leave it loose?
It's really not that big of a deal and an easy fix. Pick up and OBD reader or drop by an Autozone and they can reset the code in less than a minute. If it comes back and the cap is secured properly, have the dealer replace it. It's such a cheap fix, they won't give you a hard time. Just remember that this forum is just a small percentage of Z owners and the gas cap "issues" are not as common as you think.
Also, remember to line up the notches on the cap before turning so you don't mess up the rubber gasket.
The insurance thing is really your reponsibility, I had to do the same thing. Your agent should have a list of places that does the inspection and takes all of 10-15 minutes. You could also send your agent a copy of the bill of sale and that should be sufficient. The only reason I couldn't do that was because I misplaced the bill of sale.
Relax & Good luck with the fix.