Ford. 2.5 years old, straight from the factory. All the trimmings.
No it doesn't. The infotainment bit is entirely separate, separate screen, separate box, separate controls, separate functions. It doesn't even pull in OBD data, and the conventional dashboard doesn't pull in anything from the infotainment. There's even one set of buttons on the steering wheel for one (up/down/left/right for dashboard) and a completely different set for the other (voice, volume, track control, etc.)
I know this because the other day I had a dodgy SD card in for my music and the Ford Sync thing went absolutely ape... freezing, crashing, rebooting into maintenance mode, stopping the music for minutes and then skipping four tracks, etc. Turned out to be corruption on the SD card.
Literally the only thing it affected... the infotainment and the A/C (which is controlled by the infotainment display). I was driving at the time and continued driving without anything flagging on the dashboard or any control issues whatsoever.
Ford still make new cars that use the same isolation. Hell, you can swap out the infotainment for Android boxes online... it's a self-contained unit that gets a completely independent and isolated set of cables to read the sensors it needs to (e.g. GPS, USB, speakers, etc.) - and if you want OBD on that Android you literally have to connect it to your OBD port separately. You can pull the box entirely out, and just carry on driving like nothing happened.
So, no, modern cars aren't all doing this on the same display and cable. Anything with half a brain is isolating them.
And even if the *displays* are pulling data from both systems, that does not mean they can self-drive from the web browser. Anyone with a brain will be making one a read-only and isolating critical functions that - if they can be tampered with by something as simple as a bit of static on the user's fingers, or an MP3 crashing the music players, to the point that it can affect braking, steering, or anything else, they would be legally liable for.