Signal based navigation which gives your coordinates is also based on the stars. Whatever the signal is coming from gets its coordinates from land based stations, which themselves have a known coordinate which was based on a survey of the sky at some point. The LORAN broadcasting towers had to know their own coordinates to be able to provide ships their coordinates via radio wave, which was ultimately derived in the traditional manner from celestial bodies.
The only way to know your latitude is if it was somehow based on the stars or celestial bodies down the line. It doesn't just come from nothing.
Loran is based upon known locations on earth, that is true, but Loran hasn’t been in common use for many years. Ship owners have uninstalled the Loran receivers years ago. GPS is obviously a space-based navigation system and has no fixed location. Receivers on ships, or even in your cell phone, use the signal data transmitted by several GPS satellites to resolve the current position. The GPS satellites use built in atomic clocks to provide the precise timing necessary. This system depends on a spherical earth and the positions wouldn’t be accurate if it were not. The same goes for the navigation procedures used ancient navigators using a sextant and the sightings of the Sun, Moon, planets, or stars. These days you wouldn’t need stars to establish your position because particular spots on the earth have agreed upon coordinates. Ships are still required to carry sextants, navigation tables, and accurate maps based upon a spherical earth in case of a massive GPS failure. It’s the law.