No, I understand it. Analyzing your gas and then confirming that your computer settings match what the analysis read, is one process. Entering the water without 100% certainty of what you're breathing (and frankly, what your buddy is breathing) is a recipe for trouble, sooner or later. In this example, their profiles appear to have ended up in shallow water for an extended period, which was all "decompression". That's the nice thing about tropical reef diving... a lot of the time, the decompression just "happens" by virtue of finishing the dive noodling around in the shallows.
And with all due respect, in your comment that I quoted, they didn't actually "know" what they were breathing, because they didn't analyze their gas. They "believed" they were breathing air, because someone else told them that they were breathing air. Do what you will, but that's not good enough for this boy.
There can be exceptions of course. We're heading to a little place in Belize later this winter and they only have air, so nitrox isn't an option. Obviously, there's no need to analyze those tanks.