IO, I think you are perhaps taking my words too literally.
An ARC issue requires that all the past continuing airworthiness has been carried out etc etc and the aircraft is fine fettle. At the first ARC a company would go 'back to birth' - as far as one can. At the CAA Subpart G course I attended, the CAA agreed that it wouldn't always be possible to have all the log books, workpacks etc on hand to check this. In the case of GA machines there are rarely ADs etc carried out that can't be checked for compliance at a later date. At the next ARC, you only have to review work carried out/required to be carried out since the previous ARC.
If I hadn't seen an aircraft before and was issuing an ARC on it for the first time, I would want to satisfy myself that all ADs etc that were required to be carried out, had indeed been carried out. This may be accomplished by signatures in log books accompanied with Form 1s (for instance in the case of mag overhaul), signatures in the log book pink pages etc. No engineer is likely to accept the word of an owner that the mags had been overhauled without documented proof. It's easy enough to check with the company that overhauled the mags that the work had been carried out.
I'm not sure what the problem is with this anyway. How I choose to do my job doesn't affect the owner - we charge for a 'Star Annual' irrespective of the man hours and expense I put into the paperwork side and the amount of time I put into satisfying myself that all is well is up to me.
I'm not sure why the referral to the Export CofA is about - that too is only as good as the person carrying out the inspection just the came as any Annual or Star Annual.
We took on a Mooney for a 6 month/50hr check and there was more camshaft in the oil filter than in the rest of the engine. The aircraft had flown 1100 hours in 18 years, sitting around a lot outside, then flew a 100 hours in a year, Annual carried out and the aircraft sold. 6 months and 13 hours later it came to us for the check. It turned out that the new owner had bought the aircraft ( and flown the 13 flying hours) from a CAA licensed engineer who had rebuilt the aircraft following an EFATO (water in the fuel from sitting around outside, unflown) and a landing roll through a substantial wooden fence which (documented by photographic evidence) trashed both wings and bent one blade of the prop. The wings were rebuilt (no major problems apparent) but the engine hadn't been out for a shockload. The only documented evidence of engine work was the removal of 2 cylinders for a visual camshaft inspection. The previous owner claimed the new owner had abused the engine in its 13 hours of flying and had caused the canshaft failure. Subsequently, he did contribute to the engine overhaul costs...
My point? Not all engineers work to the same standards, that is a fact of all walks of life. What I do is ensure that, as far as is possible, aircraft leave us with everything correct - mechanical and paperwork-wise.