I wrote geosynchronous. Geostationary specifically refers to a specific kind of geosynchronous orbit at 0° latitude (equator). Geosynchronous orbits can be elliptical (as well as other types of orbits I can’t remember).
I specifically choose not to refer to them as "elliptical geosynchronous orbits” since we can’t even agree on how many satellites it takes to determine a point on a three dimensional Cartesian coordinate system.
Unless I’m missing something and you two are saying these satellites don’t continuously follow the same elliptical path.
You are correct that geostationary refers to the equatorial geosynchronous orbit, but geosynchronous still requires the orbital period to be one day. The GPS constellation is in a lower orbit, and not geosynchronous.
The debate about how many timing signals are required to determine position uniquely is pretty lively. In Euclidean space (a good approximation here), each satellite constrains the GPS unit to the surface of a sphere of radius equal to the distance computed by the time offset required to match the GPS signal.
Data from two satellites therefore constrains to the intersection of two spheres (if we don't include the earth's mean sea level as an additional reference sphere), which will be a circle with a diameter that should not exceed that of the earth itself (that nearly occurs in the case of two satellites nearly opposite each other and close to the horizon).
Data from three satellites should constrain to the intersection of three spheres, which may not exist (we disregard that solution as unphysical), occur at one point (the common unique solution) or at two points (possible but unlikely in this geometry).
However, that does not address timing error considerations, which, as have been pointed out, typically degrade the accuracy of the 3-satellite solution. Adding either the earth mean sea level sphere (approximate due to your unknown elevation), or a fourth GPS satellite sphere constrains to enough accuracy to give you a lock.
UPDATE: in case anyone is still reading - simple geometric considerations rule out the unique solution also - that would require at least one of the satellites to be below the horizon. That leaves just the problem of isolating the physically possible solution from the two points where the third timing sphere intersects the circle from the first two.