The logical conclusion of your argument seems to be that no properly flown aeroplane should crash, therefore all accidents are due to pilot error, isn't it?
I don't think that's what he's trying to say, but in the event of carb ice that can be said to be pilot error as there are many ways to stop it happening with use of carb heat, mixture and power setting. It is well documented, and if you are operating in known conditions where carb ice is rife without taking it into account, I'd say that's pilot error just as flying into a cloud and getting ice on the wings would be.
The AAIB will start at the very beginning, ruling out things like fuel contamination and pilot incapacitation early on, then look at the conditions on the day and draw their own conclusions. Obviously we don't have all that information to hand, and are purely speculating (which I again emphasise is a good thing as it may just make someone take something on board to stop an accident in the future).
History does rather show that accidents happen when lots of things line up rather than one sole cause, perhaps this scenario could be unfamiliar with the displaced threshold, sun in his eyes, grandson excitedly distracting him from the back seat, who knows maybe carb ice and an engine failure as well.