Elephant..
At least where I am we are not allowed to fly below the MSA unless under radar control or visual with the ground or flying an approved instrument procedure.
I agree. And if you are visual with the ground, you need to request either a contact or visual approach before you're allowed to deviate from the instrument approach that you've been previously cleared for.
When you are on the DME arc, you are flying an approved instrument procedure so you may descend to the altitude depicted on the arc, and any other altitude for the procedure. The key is that you must have your avionics correctly setup for the phase of flight you're in.
I'm going to specifically talk about GPS use in Canada, however, these procedures are exactly the same or very similar for FMS or RNP use around the world.
When you're within 30 NM of an airport and have an approach procedure loaded, the GPS will automatically change to terminal mode RAIM and CDI sensitivity - both being 1.0 NM. You are required to be in terminal mode when flying the initial segment, intermediate segment, and missed approach segment. The only time you are required to have approach mode RAIM and CDI sensitivity is during the final segment - between the FAF and MAP.
So as long as you are in terminal mode (1.0 NM), you may fly the entire approach up to the FAF. From the FAF to the MAP you must use the equipment specified as the title of the approach plate for lateral guidance. See this:
http://i.imgur.com/r4lyK1f.png
As long as you load the approach from the database, everything else will be done automatically. If there is any issue, you will get a warning from the GPS telling you something along the lines of "RAIM NOT AVAILABLE" and that means that you need to discontinue using the GPS for your primary means of navigation for that phase of flight. The FMS should tell you the same thing but I won't guarantee it - you need to read your FMS's manual or AFM supplement for your airplane and equipment. Nothing you ever read on the internet will ever supersede what's written in your AFM!
So, as long as the FMS Airmann was using had the approach loaded from the database and it was not giving any warnings as to its performance, then they could use it to fly the approach all the way up to the final approach segment - transition to flying the ILS from that point (in real world you intercept and track the ILS before the final approach segment) - then transition back to the FMS navigation for the missed approach if they went missed. Most FMSs will automatically transition to using the ILS without you having to push any buttons. So, after loading the approach into the FMS you'd only have to press one button for the entire procedure - (the G/A button) to get it to sequence to the missed approach.
Considering Airmann said this:
GPS was Primary and the aircraft few the arc perfectly (as it was programmed to do) intercepted the ILS landed, went to the hotel. Didn't think twice about what we had just done.
I don't believe he violated any rules. If the GPS didn't have the proper integrity for the airspace he was in it would have given him a message.