Location service uses gps (and similar satellite networks), cell and wifi info combined, so they are kind of not wrong. But it's not needed for "GPS" but it's hard to cut through the layers for people?
I often experience very slow time to fix with cell service off (& having location off beforehand) - I believe this is due to Assisted GNSS/GPS which significantly improves the time for GPS to start working (the associated Wikipedia article states that ~1 minute often without it, and worst case ~12.5 minutes)
Yeah, assisted GPS is great. I remember ye olde GPS consumer receivers taking minutes at a time to find a location while modern phones are of course much better and a lot of it is down to having a network connection to help out. It got so much better so fast that it's easy to forget how janky it could be!
A phone connection does help for downloading all the data you need to interpret the GPS signals. It's called assisted GPS. Without a connection, it can take upto a few minutes for a GPS receiver to figure out where it is.
