the phone can't detect if it's being turned around the vertical axis (not the phones but the one in relation to earth) for example. The Acceleration data doesn't change.
So your logic is somewhat flawed. If you assume that the phone's position stays fixed in relation to the car for example then it might work, since you know a car doesn't move sideways for example.
But you can't do 6DOF positioning with only linear acceleration data. You'd need rotational rate as well.