There can really only be two causes for this tuning instability: tuners or nut. I'd like to know what guitar/headstock style we're talking about, because Gibson types are the worst. Fender type headstocks with straight-pull strings thru the nut are by far the best. But IF the nut is "properly slotted" even Gibsons can be pretty stable. Carlos says that, "The grooves (in his nut) are perfectly formed", but I seriously doubt that. The technique of slotting a nut is far more important then the material used for the nut. Out of well over 100 guitars that I have made or owned and have worked on the nuts, I can count on one hand those that had tuning stability problems. Even guitars that had very cheap tuners and plastic nuts. But the guitars that DID have stability problems after I had worked on the nuts were all due to the cheap tuners. None of them that had problems were due to the nut (after I had worked on them).
So, if the tuners in Carlos' guitar are reasonably good tuners, then the slotting in the nut (no matter what it's made of) IS the problem, no matter what his luthier says. Obviously this is my opinion, but it is based on a lot of experience making and working on nuts.