There are a few misconceptions here. Not that I'm the definitive expert (so bring on the corrections) but here's a few thoughts:
- GPS, on its own, is less accurate in the vertical than in the horizontal (on the order of three to five times less accurate), but a handheld GPS typically only reports its horizontal accuracy. So most likely you just got lucky getting a reading this close.
- Reporting accuracy as a single number, even when you just consider the horizontal accuracy, is a bit of a strange idea anyway. Anybody who's had a bit of statistics knows about the "bell curve" of the normal distribution, and standard deviation. That standard deviation, or sigma, would be a better way of expressing accuracy.
- In 1984 there was a big conference, or something like that, in which the experts finally decided on the "basic shape" of the earth (not a perfect sphere, but an ellipsoid or something). Countries started to use this system, WGS84, from that time onwards, but implemented it in mapping procedures over a period of time. There's countries who haven't done it yet, even. Since the spot was surveyed in 1987, it almost surely was not measured using WGS84, so its spot height of 2053 feet may not be accurate in any case to todays standards. But your GPS will almost surely use WGS84 by default.
- There are no "sub meter accuracy" GPS units per se. All GPS units take individual measurements to the same accuracy. The difference between a handheld, 150 UKP unit and a 20KUKP survey GPS is that the handheld *expects* to be moved, so it just displays its individual measurements, one each second. (The display will become stationary, reading 0 km/h, below a certain threshold.) The 20 KUKP unit expects to be stationary, on a tripod or something, and will take measurements over a period of minutes, hours or even longer, and average out all the measurements. This can lead to centimeter precision. But that's not where the cost difference comes from: this comes from features like Differential GPS, laser range finders, inclinometers, very accurate optics and whatnot.