Yes selecting an inspector for an EICR is a problem. Anyone can say they are trained and do an EICR, they do not need to be a member of a scheme, or pass any special exams.
The C&G 2391 is considered to be the exam required to do an EICR, and the scheme providers use a different colour form if covered by them to when not. And the has been a court case Pembrokeshire County Council Trading Standards v Mr Cummins when the EICR was too brief, but he held up his hands and pleaded guilty, had he not done so, not sure they would have won, as it is a personal opinion.
When I moved into this house I wanted RCD protection and I also wanted it not to have nuisance tripping, so all RCBO I made a mistake and ended up with type AC where is said type B on the boxes, and I did fit a SPD and was happy paying the extra, but there is no rule saying I must do this.
The inspector has in the main three classes, C1 = dangerous and there is rarely an argument about this, then C2 = potentially dangerous and C3 = improvement recommended, and as long as the inspector logs a fault, it is very hard to say if C2 or C3 is wrong, lets face it, 230 volt is potentially dangerous, but it does not really matter what code a fault is given, he has highlighter the fault, and that was the bit that matters.
Only when the new landlord law came in was there a problem, as in real terms C2 means must be fixed in 28 days, and C3 means you don't need to do a thing. I saw C3 as telling the client he may need to do some thing if he want to alter the electrics, for example add a new socket, but if he leaves the existing installation alone, he does not NEED to do anything.
But I have seen reports where I can't see what the fault was, or where it was potentially dangerous but only given a C3, however since it is the inspectors personal opinion there is nothing to say he is right or wrong. But it only matters if a rental property.