I never said they didn't, please re-read my post. What I said was that it wasn't designed to give 3D positioning (because it wasn't), and that it is not very good at it (because it isn't).GPS signals allow for calculation of position, x,y & z...Elevation is available.
How do you know they are correct?? If they are +/- 10 meters it is a happy accident, because the horizontal accuracy specification is greater than that and vertical positioning accuracy (typically not quoted by manufacturers because it looks bad) is typically 1.5x - 2x the horizontal figure....and the altitude readings are very good. It's normally less than +-10 meters. That's good enough for me. I know the exact altitude at home, and TomTom always is correct within a few meters. Very good!
Rcacs, as a pilot you must be aware that GPS is never used for altitude. There is a good reason for this, it would be suicidal. If planes could reliably get a 3D position from (uncorrected) GPS, they would. They use an altimeter because they can't.
At teh end of the day it boils down to the mathematics of calculating the position. To achieve z-level accuracy approaching x/y accuracy is a pipedream. I use GPS receivers that can achieve 10cm accuracy horizontally, vertically they struggle to get 50cm.
If you are interested in learning more about the subject, there is a good starter to the topic here http://weather.gladstonefamily.net/gps_elevation.html More precise descriptions go straight into the realm of hyper-maths!!