What ever happened to good old common sense????
We've been training it out of people in the school system for decades. But, it's only now that those people we've been training it out of, are in such dire need of it.
The answer is simple. If you have not acquired the required visual reference to legally continue the approach to land, then continue on the Non-Precision aspects of the approach. For example, if only the GS failed, continue to LOC minimums, then if you have the necessary visual cues, continue forward. If not, Go-around.
If the whole ILS system shut down, provided that you have the "approach light' system in view, then you can legally continue until you have the runway environment (or however your local authority state it) in view. This could be at 4000 feet, it could be at 400 feet, or at 40 effin miles. It doesn't matter, so long as you have visually acquired the necessary references.
Your friend decided to Go Around. Personally, I'd have no problem with that. Much better to sit and discuss that Go-Around over Beer and Burgers, than to wish the hell he had gone around, but didn't.