Colour me stupid
One small planes, a normal check is to make sure the DI and compass are aligned as part of the start-up checks. When flying with a GPS a similar "does the reported position agree with where I am" sanity check during start-up is useful.
Now, colour me stupid, and I am not familiar on type, but if the inertial nav initialisation position is significantly different from the current GPS coordinates, should that not bring up a very large warning that one (or both) are not to be trusted? Or was that the initial warning that they ignored?