All this regulation reading is well and good and is there for a reason.
However, speaking as an engineer and obviously in my own opinion:-
Every job must be taken on its own merits.
The decision between AR and ID is basically
whether something dangerous might possibly happen AR
or definitely will or has happened ID
On top of this black and white decision making comes the Engineers discretion.
He or she has to decide between the two.
Looking at the scorched carpet idea, if I was in that position and needed to make a decision on whether it was safe to leave it or not, my choice would be ID ! Mainly because your carpet has scorched it just hasn't reached an ignition temperature ........yet !
Then when I go home, I can sleep easy without worrying about house fires. I suspect the BG engineer did the same and most people I know would too. ( bare in mind we haven't seen this).
If you brought the people who wrote that AR description to the property and ask them to sign their name and take responsibility for it, my bet is they would also use discretion and arrive at the same conclusion as BG
The point I'm making is, that just because it says something in a rule book, that doesn't always outway an experienced engineers decision making and does not necessarily make their decision wrong.
The fires going anyway now but as above. Log burner is hotter still and needs a registered and qualified installer.