My understanding of GPS fixes is that having the altitude assumed to be right gives a quick fix, but once you have a multi-satellite fix it is equally accurate in all directions (so say +/- 50 meters on a bad day - +/-10 on a good day for a non-EGNOS/WAAS receiver). We just perceive 50 meters vertically to be a bigger error than 50 meters laterally (and of course it is if you are trying to avoid terrain ;-)
For good geometrical reasons, the algorithm which determines height above geoid is separate from that which outputs lat/long co-ordinates. Since the primary interest of GPS users is lat/long, the WAAS/EGNOS corrected lat/long is more accurate than height by a factor of roughly 2. You have a 95% probability of being within 10 meters of the horizontal fix, and 20 metres of height above geoid. The lat/long are accurate enough for GPS approaches, but I would hesitate to rely on GPS height for the flare and touchdown.....................
