Indeed the addition of a 4th fix does not constrain the equations, I was thinking of a slightly different positioning system when I wrote that.
The 4th signal is not historically from a ground station: most GPS receivers will generate an estimated position with a low-accuracy warning on 3 fixes, but they expect 4 in order to generate a real estimate. That 4th signal is normally another satellite. I did look briefly for the difference in CEP-50 between 3 fixes and 4, but could not find a source. You have not linked to any previous discussion on this subject, or external references, so if you have numbers on what the real difference between 3 and 4 fixes is then they would be interesting.
Ground stations are used in d-GPS, but not only as an extra point of reference. As an known location they can be used to cancel errors in the satellites estimate of its position.