Rumet,
I agree with your summary.
How did that 4000' disappear?
Yes, a crew “knowledgeable of the locale” probably should have done a go-around.
But the peculiar thing is that on airports with certain topography, some types of glide-slope guidance equipment might suck you in. I wish I knew how the “voting rationale” on an FMS works . . . and when it decides to tell you, “You-take-it”!
If this flight was “slotted in” on a shot-final (5 nM?) . . . and if the altitude was a little too high . . . what does the FMS do when it never receives a “fly-down” from the glide-slope transmissions?
RESA