Sure. I was trying to point that out without going into all the maths.
GPS, crucially doesn't give you a position (x,y,z). It gives you a position, and a time.
To get an position with lat/lon, you need at least 3 satellites, as you need to solve the equations and have pop out lat/lon/time.
This is because, as you say, you get only differences in ranges.
But, with three satellites, you can unambiguously determine three factors. (if you assume you're at a known altitude) Lat/lon and time. Or lat/alt and time, or ...
If you have four satellites, you can determing lat/lon/alt and time.
However. If you have more than four satellites, you can look at the residual errors.
For example, if you have 10 satellites, and do a best estimation of the position leaving out one satellite from the computation each time, and find that they all fall within a 2m circle, except satellite 3, which if you include its value, causes the position to jump 20m, you can discard that satellite. (or in practice, weigh it really low)
The error estimation inside a GPS is complex, it knows what the error per satellite 'should be' in the ideal world, and then tries to compensate for known problems - for example if all the satellites are on one side of the sky that reduces precision, and is fairly easily calculable.
In some cases, the position error can be misleading, as all the information the GPS has leads it to believe that it's the same position.