EPE is generally based solely upon the geometry of the satellites assuming ideal signal reception. Thus it is at best a lower bound on the expected error and at worst, complete fiction.
DOP = dilution of precision (based upon satellite geometry)
EPE = DOP * EPE_ideal_conditions
EPE_ideal_conditions considers errors from many sources (noise, uncertainties of signal propagation, etc)
EPE is a standard concept in GPS position measurement. (The formal definition is x% probability of being within the given distance of the true location. 90-95% probability is approximately 2 standard deviations.) There are 3D, horizontal (2D), and vertical error bounds. (EPE is the 2D horizontal.) Garmin may have a proprietary version, but the concept and a number of methods of computing it are quite public.
A rule of thumb is that the vertical estimated error is on the order of twice the EPE (subject to the same caveats above).
A typical EPE for a consumer GPS is 95% probability of being with ~30ft (thus vert ~60ft). Therefore both measurements (4033 and 4058 ft) are consistent (within a probability of 95%) with a true altitude of 4025 ft .
A typical consumer GPS will not allow us to establish a better altitude for Owl's Head than the USGS topo. That would require a survey grade GPS with a qualified operator at the helm. And possibly many hours of signal collection.
I outlined several methods (barometric and water/beer hose) for measuring small differences in altitude for 2 fairly close points which might give us amateurs a shot at finding a better "true summit", but these methods will not help us to measure the absolute altitude.
A non-GPS method for determining the absolute altitude would be to compare the barometric pressure to that at a known nearby location (such as an airport). Big airports transmit the effective sea-level pressure on ATIS (automatic terminal information service) radio so that aircraft can set their barometric altimeters. (Whitefield seems to post the data hourly on the web, but I don't see a listing for an ATIS radio frequency.) This would require temperature and humidity compensation for maximum accuracy. I don't know what the accuracy of this method would be.
bobandgeri:
The summit pictures of your gps are consistent with a reading to the accuracies described above. However the satellite display and EPE can fairly reliably tell you when you have a bad fix, but cannot reliably tell you when you have a good fix. There is an effort (RAIM--receiver autonomous integrity monitoring) by the FAA to develop methods for guaranteeing the accuracy of a GPS reading. WAAS (wide area augmentation service) is part of this system.
Doug