I know how worried you are, I felt the same way when I got my new 2013 and it had 263 Gid at the dealer. I was bummed and felt like I'd made a mistake taking delivery of the car. It turned out there was nothing wrong with the battery. Some of the 2013 cars show low Gids on a Gidmeter and Amp Hours on the LeafSpy, but the batteries seem to have the same capacity and usable range as any new LEAF. It appears that these cars just show different readings than the older cars that we've come to regard as expected for a LEAF.
There are a couple of threads here that would be worth a read for you, especially one titled "2013 Low Capacity.. "
The bottom line is that several of us, including myself and stjohnh have carefully evaluated 2013 LEAFs that show these kinds of low readings. We've shown that the cars have the full range autonomy and capacity expected. We've done this by driving the cars at a controlled speed of 100 km/hr over a round trip course and achieving expected range to Turtle of about 88 miles. In addition, I measured the kWh required to recharge from Turtle, and it matched the expected capacity of about 21.5 kWh after allowing for charging losses (actual measured energy used for charging was about 26 kWh).
So when I suggest that you not worry too much, I'm speaking from experience.
Here's the kicker, though: In our cars, we found that we needed to take the car down to Turtle to see the full range. These cars acted like they were storing more energy than expected below VLBW, and we get several MILES of range below a reading of 10 Gids! This us NOT a good thing, obviously, because most of us want to park it at VLBW, and from what we've seen, you'd be sacrificing 8 or more miles of range if you stop there. But that's what we've found, and once you know how your car will behave at low SOC, you can live with it quite happily.
I also found that several charge cycles up to 100% without an end timer gives the pack a chance to balance better, and your Gids should rise. In fact, during a long trip with several successive 100% L2 charges over two days, I saw a Gid reading of 284! Weird but true.