I feel like that's not a true cold GPS signal! Though I'm not arguing the parents scenario is realistic either. I got a GPS module for a drone I was building and it took 20 minutes to get a proper GPS lock from cold!!! I was sitting there watching betaflight doing it's thing wondering why the heck it takes so long when there's so many satellites in view!
You're right that it's not a true cold GPS signal. I've connected to the network in the last 180 days (and thus have information on satellite information), I have a rough clock (time within 20s or so). The phone probably assumes it's closeish to where it last turned on. Etc.
It is the realistic scenario that people would face without using WiFi routers or cell towers though. True cold fixes aren't something phones need to deal with basically ever.