I'm a fan of GPS, but I know that they can sometimes give inaccurate readings. Fortunately, I haven't had anything as scary as this happen to me, but I know that there are limits to how accurate they are.
For instance, one source of limited accuracy is shortly after a receiver is switched on, as it aquires satellites - it can take up to several minutes to aquire enough (at least 3 for just latitude and longitude, at least 4 if you want elevation too).
Another issue is visibility of the sky - I remember being in Lower Abbey Street, Dublin and noting that my trackpath, taken literally, had me wandering north, through some stone walls. This was due to much of the sky being blocked, some signals probably reflecting off buildings and possible diffraction of the satellite signals by the edges or corners of buildings.
Tree coverage can also cause problems with accuracy.
High accuracy is possible if you can get EGNOS or WAAS satellites on your receiver - that can get accuracy below ten metres, but most of the time ten metres is what you usually get.