One thing that Google does is estimate your location based on the WiFi networks around you.

When Android phones connect to the internet, they send to Google the details of WiFi networks nearby. If a user has their location (GPS based) turned on, the phone will send it’s location along with the WiFi networks info.

Google is then able to build a database from many user’s location with the networks they had around them. If your phone has its WiFi on (even if it isn’t connected to one), it tells Google “I see these networks around me” and then Google is able to tell your phone that based on the ones you are seeing you are probably in X location because users in that vicinity have seen the same networks.

The same thing can be done for cell phone towers so even if the phone has WiFi turned off, it can estimate a location based on the cell phone towers it is seeing.

So it is possible for Google to give you emergency alerts with precise location turned off but they probably have treated alerts as an “all or nothing thing” where you give them all your location data or you don’t get the alerts. I think their legal justification for not providing the alerts is that you can get alerts from non Google products (radio) and the precise location requirement is “vital” to make sure the right alerts are getting to you.