You are absolutely correct, one must work to the standards, and if a customer were to have gas Safe inspect a job, everything not correct would be subject to demand that you alter it. But, if a GS inspector were to spot a vent too close to a boiler, or a cooker point in the incorrect position, he still would not apply the AR procedure - because those situations are classed as NCS.
So, faults that you come accross have to be assessed for safety, and you must decide in which category it falls. Even of the job is 2 weeks old, it is existing. Not every fault is classed as at risk, but things like fumes are not as black and white as, say, a cooker point. I suppose my main ssue with this situation is "why would you leave it, if you fee l is AR". If you apply AR properly, the appliance is only turned off at the customer control, the customer then decides whether to use it or not. It is often quicker to sort out problems than complete the paperwork, explain to the punter and field all the arguments.
If an RGI spotted the cooker hose, he would either note it as NCS or ignore it. Or, obvioulsly, quote to rectify. You cannot INSIST that the work is done, and it would be wrong to do it, charge and tell the customer that youwere required to do it. You cannot invoke an AR procedure because it "looks wrong", to CYA, or "to err on the side if safety". You will struggle to get paid for the paperwork etc, whereas you can legitimately charge for the rectification - provided you have set up your systems properly. In this case, TBF, it may have been more awkward as the terminal is in the neighbours garden.
In short, you have the concept and practice of the Unsafe procedure slightly muddled. I am not trying to have a go at you, you are not unique and one has to gain experience. Unfortunately, there are a lot of experienced guys who get it wrong, especially on this forum - but be careful not to follow the herd.
You say you have not got the book? You don't really need it, as it is all online. (I assume you have seeen the online version?) If you do not carry a tablet, then it is worth buying the printed version, even if it is to be able to show an argumentative customer.