GPS altitude uncertainty is (I think) a factor of 3 greater than the horizontal position. Because it's often obvious what your altitude is, it highlights the error.
As mentioned, GPS tells you your position relative to some chunks of metal orbiting the earth and knows nothing of the earth's surface. It has a model of the earth's surface which is used to estimate your position relative to the earth's surface and express it in longitude, latitude and altitude. On most GPS you can select the model it uses.
When you consider it's triangulating between satellites 12,600 miles away orbiting the earth twice a day, an error of 65 feet is put into perspective. 8-)
I was testing a GPS mapping system for mobile phone coverage in the early 90's and couldn't believe that when I had taken a drive, the trace of where I had been overlaid perfectly onto a 1:25K OS map. I'm not sure whether I was more impressed with GPS or the OS map. I later found out that SA had been turned off.
Incidentally, I spent a week on this project and got all the kit installed in a survey van and working perfectly. Customer picked it up and promptly put it on its' roof on the way home.

Kevin