I think it was an unfortunate selection of terms when it was called the competent persons scheme, it implies those who have not become a member are not competent, which it not true.
There is also the phrase new circuit, to make a circuit current needs to flow, normally controlled by a switch or rely, once it has flowed once, if it flows again it's not new, and the book says a circuit is considered formed when an over current device is used, i.e. fuse/MCB/RCBO it is not clear if a RCD forms a circuit as it is an over current device, but not through the circuit, but from the circuit to something outside the circuit. However the way it says circuits must be created to "reduce the possibility of unwanted tripping of RCDs due to excessive protective conductor currents produced by equipment in normal operation" it would seem it is considered as forming a circuit, but is this an IET definition or a government definition?
So if you plug in a new device that has never been used before it forms a new circuit, however one would hope every appliance sold is tested before being sold, so at least some parts will have been forming a circuit some time in the past, so it is not a new circuit, but an old circuit modified, in other words to form a new circuit in the home is rather rare. However we know this is not what the law maker intended when they used the phrase "new circuit" so the law needs to be added to using case law, so some court has to rule as to if adding a FCU is a new circuit.
As normal scheme providers, and other what we consider official bodies have tried to clarify the law, but putting it simple, they can't, it needs to be a court, so if a scheme provider tells its members fitting a FCU is not considered as a new circuit we do not need to issue a compliance certificate for that work, likely courts of law would accept that as coming from an expert witness. So they would rule the same, but until a court has ruled, then we simply don't know, we can only guess.
We have had some daft laws, the one on import of peanuts is the one normally given, normally thought as gobbledygook, and we are seeing this at the moment over travelling into Wales to exercise, so you can't take a run around Chester football ground as part is in England and part in Wales, but likely the ground is all locked up anyway, so it will never happen.
The same with what is a circuit, unless some very officious council guy takes some one to court, the court will never rule on it, and faced with £100 plus vat to notify the work or a court case, it is highly unlikely there ever will be a court case. However I have said so many times, few people want to be involved in a test case, there are some, the women who broke into the nuclear submarine for example, but most don't, so likely in 20 years time the same questions will still come up, what is a "new circuit" and we will have the same answer, no one knows.