My question is whether there has been a bit of "star-spangled-bannerism" leading to unrealistic optimism about USN gunnery.
Nope, it's just what can happen sometimes in any game you play, and at different points in the same battle. Gun accuracy is affected by a huge number of variables that are constantly changing independently of each other. The result is that in any 1 given period of time, individual ships can shoot quite well or quite poorly. The same ship can go through hot and cold streaks in the same battle. Some days, BCF shoots better than I.SG at least for a time, to take an extreme example.
Because of that, it takes lots and lots of test runs, under the same conditions, to determine what the actual hit rate is for any of the several types of fire control systems and methods.. As Barkhauer said, something on the order of 100 runs of the same test over and over.
When we made the original Jutland, I ran such tests for the Germans and British. And I had to do them many times over after each tweak of the fire control systems, until we finally arrived at long-term average hit rates very close to what Campbell says. And let's face it, there's really not a whole lot of other data to work from for 1916. But Campbell is great because that was under combat conditions, not target practice, and the game is about combat conditions.
So then we did the US ships. Given that the USN fought no fleet actions in WW1, there's nothing at all for detailed combat accuracy data for it at that time. We thus had to do a lot of extrapolation and, to be honest, SWAGging. The bottom line is that, over the long haul, USN BB accuracy averages out between RN BBs and BCs. IOW, their shooting is pretty mediocre.
However, as Saddletank said, the peculiarities of USN gunnery methods have a strong effect on any one run of a test shoot. In general, USN ships are slower to find the range and can't keep it as long as RN and KM ships. However, because of their wider spread and more shells per salvo, they can often get hits where the other ships would get near misses or straddles. IOW, USN ships have a wider margin of error when they're close to being on target, but they usually have trouble staying there and once they lose the range, it usually takes them longer to get it back.
As a result, most of the time, when USN ships find the range, they tend to hit with more salvos while they have it, but these relatively short periods are spread out between long intervals of groping for the range. Thus, on average, USN have an overall lower hit rate. However, when a USN ship is on a hot streak, its target is going to suffer many hits in quick succession.
That last point is pretty important. Ships have only so much damage control ability at any given time. Thus, when ships get hit many times in quick succession, damage control is only able to deal with some of the problems at once, not all of them, or perhaps only a little on each of them. And some problems get worse over time if left insufficiently attended to. IOW, a ship that gets hit 10 times over half an hour will usually take less total permanent damage than a ship hit by the same 10 shells in the same places but only over 5 minutes. This factor can make USN ships more dangerous than their rather mediocre overall hit rate would otherwise warrant, especially when they're able to hold the range for longer than usual.
But OTOH, the USN burns through its ammo at twice the rate of the other navies. Thus, cold periods hurt the USN more than other navies because they waste twice as many shells. Then, of course, the higher rate of fire really limits the combat endurance of USN ships, whether they're hitting or not.
The net result is that USN ships are the least predictable of any in the game so far. On average, they're mediocre, but their full broadsides amplify the effects of them going hot and cold. When they're good, they're quite good, but when they're bad they're terrible. But either way, they can't spend all day trading broadsides because they run out of ammo twice as fast as the enemy, regardless of which side they're on.