Yes, Vixen, this is elementary celestial navigation which many of us are trained to do. With the corrections that
@Andy_Ross has noted to your method, and the additional corrections I've provided, it describes one method for fixing your position on Earth's surface.
You need a sextant for measuring the altitude of objects above the horizon and the angular distances between other objects. You need a chronometer set to local noon at a known meridian. English sailors used Greenwich. French sailors used Paris until 1914. You carry the chronometer with you so that you know the time of local noon at your reference meridian. Ships usually carried two chronometers and averaged their errors.
"Local noon" is the exact moment that the sun is overhead—i.e., has reached its zenith. You measure that with your sextant. By noting the time on the chronometer at which local noon occurs where you are, you will know how long it has taken the Earth to rotate to bring the sun directly overhead at your location. Since Earth rotates at 15º per hour, you will know the angular distance (i.e., longitude) from your reference meridian.
You can find your latitude by measuring the altitude of the sun at local noon and correcting it via known seasonal declination. Vixen's thought experiment includes likely knowledge of the date; they abandoned ship "a few days" earlier, which presumably is a known date. However, to achieve the accuracy she claims in the latitude, you need reference charts for the seasonal declination for that date. Her thought experiment mentions none of that.
Alternatively you can sight the star Polaris at night to get latitude more or less directly, assuming you're in the Northern Hemisphere. But obviously then you can't use the sun to determine your longitude. At night you can use "lunars" (provided the Moon is up) to determine longitude, but that too needs reference tables to convert the position of the Moon relative to background stars to a time reference.
So no,
@Vixen hasn't given you a credible terrestrial navigation solution.
We've also asked her what she means by "geopositioning." The use of various navigation methods to locate you on the surface of Earth's spheroid relative to some fixed point is the correct definition of "geopositioning." You're right in that it has absolutely nothing to do with transmitting TV signals to Earth. She's trying to fabricate something that somehow means she wasn't wrong to use the word "geopositioned" to talk about spacecraft.
Whether she realizes it or not, she has introduced the notion that rotation of a sphere at a constant angular velocity can determine angles subtended by fixed points on that surface over a given time duration, and consequently linear distances along the circumference of the sphere. If she does realize it, then she thinks she has to explain geostationary orbits from first principles. Allen and Weaver have something to say about that, but we'll see whether she is able to figure it out.