The "should not" is an opinion - SAFs - made with the benefit of hindsight. Nothing more.
It's also worth noting that SAF was acutely aware of the effect Sir Matts continued presence around the club had on his immediate successors. I think SAF made a conscious decision to try and avoid that scenario reoccurring.
I'm not convinced that comment was made from hindsight, but either way there are two possibilities, the club either knew in advance that Moyes wanted to change the staff or they did not, but whatever they allowed this to happen, and I would suggest that this should have been discussed prior to hiring.
If then board did not want to accept his condition Moyes could either live with it or walk, I can't accept that this is just the way it is done then to blame Moyes when it goes wrong. To say that he got rid of those that knew the club but those he bought in didn't is to pass the buck as the board would have been fully aware that the replacements had no previous involvement with the club.