The reason you need an accurate altimeter for this ILS is that the obstacle clearance surface for the intermediate segment - the part where you're flying straight and level without a glideslope - lies atop the very mountains these pilots crashed into. Vertical guidance on the missed approach is also barometric, and there are mountains in that direction too.
The only thing you need a precision altimeter setting for is to determine the safe decision altitude (point at which you need to see the runway environment to continue, else initiate a missed approach) and a fairly theoretical chance to intercept a false glideslope lobe.
With the clear weather, knowing the decision altitude with precision was not important and the false glideslope is easy to identify by comparing outside view and descent rate needed to stay on the glideslope.
I'm not sure of ATC's rules, but my assumption is that they would NOT clear me for an ILS approach in this circumstance. But that's moot, I would not ask for it because it's not authorized anyway. It would be a visual approach, we'd just happen to fly the ILS course and use the GS for vertical guidance.