Nobody ever reported a problem with the follow me truck at FSDT airports, and I've tried some, and the problem doesn't happen.
When this problem happens, it's likely a mistake in the AFCAD, like orphaned nodes, non-connected parkings, overlapped nodes, overlapped parkings, etc. so GSX can't find a proper path to reach a parking, and will discard illegal path segments, which will result in taking shortcuts into the grass.
In any case, there are no such errors in FSDT airports so, in that case, it might due to another AFCAD being used instead of the FSDT one, due to a conflicting scenery.
In another airport, especially non default, changes of errors in AFCADs might be more likely, because such errors might not be noticed with AI airplanes (maybe an AI disappearing or stuck might not be noticeable), but they will if you are following a GSX vehicle.
