How do you know he was 'miles off course'? I'll bet he wasn't.
All airports, aircraft, and even crews have different operating limits. Because I regularly operate in areas in which fog is common, I'm qualified to CAT IIIB...which is an automatic landing in virtually zero visibility. Most pilots (aircraft and airports as well) do not need this qualification, and so they don't have it. It's expensive in training to get and to keep, and requires equipment in the aircraft and on the ground. The vast majority of runways don't have this equipment..it only all comes together in places like London Heathrow.
The airport you are talking about has only a few airline movements per week, and so no money is going to be spent on expensive ground installations. All that it has is an NDB (non directional beacon) and DME (distance measuring equipment), both of which are extremely old nav aids. There are a couple of GPS arrivals available, and they will supplant the DME, but without a transponder installation at the airport, they won't get you much lower (if at all) than the older approaches. They are easier to set up and fly though.
Basically though, you need around 3 miles of visibility from the runway. If you don't have that, then you can't continue past the 'missed approach point'. From that point, the aircraft will be flown manually.
Ah, the computer does everything. They exist to help, but in themselves don't generally allow operations in conditions that couldn't be done manually. They make life easier and more consistent...until they screw up of course.
I'd hazard a guess that he flew an RNAV (GPS) approach to runway 04. The missed approach point is at 1.7 miles from the runway, and involves an immediate climbing left turn. You probably wouldn't get closer than a mile at the minimum, and by the time you could see the runway from the cabin would be well offset.