And where are those corrections taken into account in this page?
The author actually mentions a third source of relativistic error without saying it's relativistic error: the Sagnac effect. ("Originally, by not transforming satellite positions from earth-centred-earth-fixed (ECEF) to earth-centred-inertial (ECI) coordinates, I was effectively ignoring Earth's rotation during the 60 to 80 ms that signals were in flight.")
See also:
http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_P...
However, yes, relativity further complicates it.
"Were there an infinite value for the speed of light, light itself would not exist at all."
http://www.scientificamerican.com/article.cfm?id=why-isnt-th...
The speed of light is strange in that it has the same value independent of the relative velocity between the source and the observer. This fact is an experimental one that can only make sense if relative motion changes the relationship between space and time intervals to keep the distance covered by light per unit time the same for all observers.
The fact that space and time must get mixed up to keep the speed of light constant implies that, in some sense, space and time must be the same, despite our habit of measuring space in meters and time in seconds. But if time and space are similar to the extent that they can be converted one into the other, then one needs some quantity to convert the units--namely, something measured in meters per second that can be used to multiply seconds of time to get meters of space. That something, the universal conversion factor, is the speed of light. The reason that it is limited is simply the fact that a finite amount of space is equivalent to a finite amount of time.