At least the local data can be accessed with OBD interfaces [1] most of the time. I don't know about stuff like theft prevention where the GPS location of the car is being constantly transmitted over GSM/UMTS/LTE, though.

1: https://en.wikipedia.org/wiki/On-board_diagnostics

Typically, the manufacturer's diagnostic tool can download data from the fast stop recorder. An accident investigator should be able to access it for you.

You can get a connector and software and access pretty much anything on a laptop plugged in to the diagnostic port. Of course that software isn't free, and it's generally sold to repair shops so don't know how easy it would be for a consumer to buy.

We use Metromile for our insurance and the tracker we plug in has access to that info which they make available in a simplified form in their app.