It seems even better than that. My phone can tell me which side of a small road (2m accuracy) I am on 95% of the time. Maybe it uses a WiFi database and dead reckoning to improve on pure GPS.
AGPS is designed to give a quicker Time-To-First-Fix (TTFF) but the accuracy is unchanged.
The application here (driving) constrains the solution to 2D (i.e. known altitude from the map), and hence can since that variable is known quite accurately it can improve the accuracy of the other variables.
Receivers tend to be built with augmentation systems. This uses a network of ground stations that measure the variation in the GPS signal and transmit corrections over an additional satellite. This helps the device account for atmospheric interference.
GPS and location systems designed for driving will 'snap' to the correct side of the road.
They're aware of what they're being used for and optimise for that. Similarly, because driving is 2D solution instead of 3D, the altitude will be used derived from the map, not the signal.
Which is why GPS systems designed for driving are fundamentally not suitable for use in (say) planes which need a true 3D solution.