Altitude calculations on the SP III and SP 26xx are derived entirely from the position determined by satellite data, no reference is made to the maps at all.
The calculation is done using the WGS 84 spheriod model of the earth, which interpolates the shape of the spheriod from the equator to the pole.
So, when looking at the altitude display, you have to allow for the slight error that may exist due to the spheriod interpolation, then allow for whatever error might exist as a result of satellite geometry (quality of reception, number of satellites, etc.).
My experience, measuring it against known airport elevations, it that it is usually accurate to within about 50 feet. I compare it to the altimeter in the aircraft I fly. So, your report of -53 feet in the Channel is reasonable.
Just as a point of interest - GPS precision approaches are just being introduced for testing in some regions of the world that have either WAAS or local signal augmentation. Although these forms of signal augmentation can nail the lateral position down to about 3 feet, vertical position remains a problem - so, precision GPS approaches allow a decision height of only 250 feet above ground level, compared to 200 feet above ground level for precision approaches (Cat I) that use ground based navaids.
PanEuropean