Firstly, the coordinates stored in most GPS units are those of the aerodrome reference point and not those of the runway threshold(s). Second, obstacle clearence off centerline does not even come close to the kind of minimum that you have in mind.
I think this depends on the aircraft you fly and the equipment installed. I used to fly Fokkers. Some had really smart FMS's which allowed you to fly to runway thresholds, with varying degrees of success and some would take you pretty close(ish). In each case, a reasonable planting on an airfield could be guaranteed but you would have to manage the vertical profile yourself. But I now fly an Embraer and a fit that would allow a very accurate (but not approved) planting on a runway and the beast would manage the vertical profile for you as well (quasi-ILS). Obviously I'd prefer not to be in such a compromising position in the first place, but if I had no other option I'd go where ever I could get the best RFF/runway/weather/obstacle combination (and as few lawyers as possible).
PM