Unless you have a smancy-fancy sat receiver (simultaneous multichannel GPS, Glonass, Gallileo + assisted, etc.), you don't get precision down to a few CM.

Most of the satnavs (including Pure Maps) do "snap to road".
They assume you're still on the road and not 1m outside of the road as current GPS position gives (due to errors, not enough visible sattelites and/or urban canyon).
So they automatically "map" you to the closest road.

The autorotation hapening despite you not taking a turn is simply the satnav guessing wrong when trying to "snap to road".

Using the in build accelerator would be an extremely crude and unreliable way to guess if a change of direction occured.

(Compass heading change would be better.
The best would be to ask the AI running on the camera for cars that have LDAS/FCAS.
Anyone motivated to port Comma.ai's Openpilot onto Sailfish ?)