Peter:
4" Squares are now in the marketplace here (NJ) with 'dimpled' marked tapped holes for grounding screws to prevent your scenario of the Hilti installation.
Personally, I have never seen anyone put a grounding screw in the 'side' holes, and some may say that is a technical violation; the rear tapped hole has a "grd" marking stamped in by the mfg.
So much for splitting hairs!
Bob; MHO on your original ??; if the box is mounted thru the side holes ie: pic#3, I would not have a problem with it, as long as the box is flush/square/plumb and secure.
John